24 adults, between the ages of 18 and 75 years, with cerebellar ataxia will be enrolled in a 12 week trial of BHV-4157 for treatment of ataxia. BHV-4157 is a pro-drug of riluzole (which is currently FDA-approved for ALS, Lou Gehrig's disease). There will be 5 visits to UCLA required--Screening when general and neurological examination, blood and urine testing, ECG, and questionnaires will be administered; Baseline when general and neurological examination and questionnaires will be administered and study drug dispensed; Week 4 and Week 12 when general and neurological examination, blood and urine testing, ECG, and questionnaires will be administered; 2 weeks after finishing study drug when general examination and blood testing will be completed. There is an option for a 36 week extension of the study drug trial.

Inclusion Criteria:

1. Informed Consent a. Subjects (or legally acceptable representative as required by the IRB/IEC) must provide a written signed informed consent form/forms (IRB/EC specific) prior to the initiation of any protocol required procedures.

2. Age and Sex a. Male and female outpatient subjects between the ages of 18 - 75, inclusive

3. Target Populations

   a. Subjects with (1) a known or suspected diagnosis of a specific hereditary ataxia: SCA3/dizziness-predominant or SCA1, SCA2, SCA3, SCA6, already taking Riluzole for more than 8 weeks; (2) non-genetic pure cerebellar ataxia; (3) MSA-C: i. SCA subjects should have confirmed genotypic diagnosis from a CLIA-certified lab or a family member that has had such testing.

   ii. Alternatively, subjects must be willing to undergo genetic testing from a CLIA-certified lab if testing has not been previously done on the study subject and a copy of results is not available for verification.

   b. Ability to ambulate 8 meters without assistance (canes and other devices allowed); c. Determined by the investigator to be medically stable at Baseline as assessed by medical history, physical examination, laboratory test results available in medical record, and electrocardiogram testing available in medical record. Subjects must be physically able and expected to complete the trial as designed; d. Minimum of 6 years of education; e. Subjects must have adequate hearing, vision, and language skills to perform interviews as specified in the protocol; f. Subjects must be able to understand and agree to comply with the prescribed dosage regimens and procedures; report for regularly scheduled office visits; and reliably communicate with study personnel about adverse events and concomitant medications; g. Women of childbearing potential (WOCBP) and men must be using an acceptable method of contraception to avoid pregnancy throughout the study and for up to 30 day after the last dose of investigational product in such a manner that risk of pregnancy is minimized. The requisite drug interaction studies to determine the interaction of BHV-4157 with oral contraceptives have not been performed to date. It is therefore not possible to determine the efficacy of oral contraceptives as an effective method of contraception for WOCBP who participation this study. Oral estrogen and progestin hormonal contraceptives as a sole method of contraception are therefore prohibited. It is required that all WOCBP use two methods of contraception for the duration of the study (i.e. beginning at first treatment to 30 days after the last dose of study drug).The two methods should include one barrier method (ex. condom with spermicidal gel, intrauterine devices, cervical cap etc.) and one other method. The other method could include oral contraceptives or another barrier method.

   h. Women of childbearing potential must have a negative serum pregnancy test at screening and a negative urine pregnancy test within 72 hours of dosing.

   i. SCA subjects (SCA3/dizziness predominant; SCA1, 2, 3, 6 on Riluzole for more than 8 weeks) will not be limited to Inclusion Criteria of Screening SARA score ≥8 or Score of ≥ 2 on gait subsection of the SARA.

   j. Non-genetic pure cerebellar and MSA-C subjects will be limited to Inclusion Criteria of Screening SARA score ≥8 or Score of ≥ 2 on gait subsection of the SARA.

   Exclusion Criteria:

1. Target Disease Exceptions

   a. Any medical condition other than one of the hereditary ataxias specified in the inclusion criteria that could predominantly explain or contribute significantly to the subjects' symptoms of ataxia (for example, alcoholism, vitamin deficiencies, multiple sclerosis, vascular disease, tumors, paraneoplastic disease, head injury, idiopathic late onset ataxia, multisystem atrophy) or that can confound assessment of ataxia symptoms (for example, stroke, arthritis); b. MMSE score < 24; c. Subjects with prominent spasticity or dystonia that meet either of the following criteria: i. In the opinion of the investigator will compromise the ability of the SARA instrument to assess underlying ataxia severity; or, ii. Are associated on the INAS instrument at screening with moderate or severe scores on dystonia (at least 3 of 5 items) or spasticity (at least 2 of 3 items) or rigidity (at least 2 of 3 items) d. SARA total score of > 30 points at screening; e. Subjects may not have started physical or occupational therapy within one month of screening and are not expected to start such therapy during the initial 12 week treatment phase. Subjects with ongoing occupational or physical therapy may be allowed to continue as long as the intensity remains unchanged from two months prior to screening throughout the randomization period.

2. Medical History Exclusions

   a. Clinical history of stroke. Note: Subjects with a history of transient ischemic attack (TIA) may be enrolled, if it occurred at least 3 months prior to screening and the subject is prescribed appropriate treatment [e.g., platelet aggregation inhibitors]; b. Immunocompromised subjects. Note: Subjects taking a systemic immunosuppressive agent may enter treatment phase if they are on a stable dose, have no clinically relevant immunosuppression, and have a white blood count (WBC) within normal limits; c. Active liver disease or a history of hepatic intolerance to medications that in the investigator's judgment, is medically significant; d. History of medically significant gastrointestinal (GI) illnesses including: i. A current diagnosis of active, peptic ulceration or gastrointestinal bleeding within the last 6 months and/or chronic inflammatory bowel disease at screening; ii. A history of any gastrointestinal surgery that impacts the absorption of study drug; iii. Chronic or frequent episodes of loose stools; bowel movements; e. Vitamin B12 or folate deficiency Note: Subjects with a B12 deficiency can participate in the study if they are on stable Vitamin B12 replacement for at least 3 months prior to randomization and their B12 levels are within normal limits prior to randomization; f. Hematologic or solid malignancy diagnosis within 5 years prior to screening. (Note: Subjects with a history of localized skin cancer, basal cell or squamous cell carcinoma, may be enrolled in the study as long as they are cancer free prior to randomization. Subjects with other localized cancers (without metastatic spread) who have previously completed their course of treatment more than 2 years prior to baseline, are not currently receiving treatment and have been in remission may be enrolled only if, in the opinion of the investigator, there is no expectation for recurrence or further cancer treatment during the study period. Antihormonal therapy (e.g., tamoxifen) is allowed if the subject's cancer is in remission and the subject is on maintenance therapy to reduce their risk of recurrence; g. Any unstable cardiovascular (includes uncontrolled hypertension), pulmonary, gastrointestinal, or hepatic disease 30 days prior to screening; h. End-stage cardiovascular disease (e.g., Congestive Heart Failure New York Heart Association/CHF NYHA Class III or IV or unstable angina); i. Treated for, or have had a lifetime diagnosis of, schizophrenia or bipolar disorder; j. Active major depressive episode within the past 6 months. Note: Subjects on a stable maintenance dose of a non- tricyclic, non-monoamine oxidase inhibitor (MAOI) antidepressant medication (e.g., serotonin reuptake inhibitor, bupropion) with symptoms in remission may be eligible; k. History of neurosyphilis (as indicated by a positive rapid plasma reagin [RPR] test and a positive confirmatory test); l. History of drug or alcohol abuse within 12 months as defined by DSM-IV-TR-TR criteria; m. History or evidence of any medical, neurological or psychological condition that would expose the subject to an undue risk of a significant adverse event or interfere with assessments of safety and efficacy during the course of the trial as determined by the clinical judgment of the investigator; n. History of chronic pulmonary disease or chronic pulmonary symptoms

3. Physical and Laboratory Test Findings

   a. Uncontrolled hypertension at screening (e.g., repeated diastolic measurements ≥ 96 mmHg); b. Subjects with history of hypothyroidism may participate in the study, provided they are euthyroid on stable thyroid replacement therapy for at least 3 months prior to Baseline, and therapy is expected to remain stable during the course of the study; c. Hepatic test abnormalities at screening: i. Aspartate Aminotransferase (AST), Alanine Aminotransferase (ALT) or GGT > 2 times the upper limit of normal; or ii. Total bilirubin > 2 times the upper limit of normal (ULN); d. If diabetic, HbA1C > 7.5% within 3 months of screening; e. Pathologic renal findings at screening as defined by the presence of either of the following criteria within 3 months of screening: i. Estimated glomerular filtration rate (eGFR) according to the re-expressed abbreviated (four- variable) Modification of Diet in Renal Disease (MDRD) Study equation < 30 ml/min/ 1.73m2; The MDRD estimation is calculated as follows: eGFR (mL/min/1.73m2) = 175 x (standardized Scr)-1.154 x (Age)-0.203 x (0.742 if female) x (1.212 if Black). [Scr: Standardized serum creatinine] ii. Quantitative urine protein/creatinine ratio greater than 0.2. This test may be repeated if clinically indicated. In the event of a urinary tract infection (UTI), the test may be repeated after the UTI has resolved; f. Hematologic abnormalities within 3 months of screening: i. Hemoglobin < 10 g/dL; or ii. WBC < 3.0 x 103/mm3; or iii. Platelet count < 100,000/mm3; g. QTc (Bazett's) and QTc (Fridericia) interval > 480 msec within 3 months of screening and confirmed by repeat measurement or uncontrolled arrhythmia or frequent premature ventricular contraction (PVCs) (> 5/minute) or Mobitz Type II second or third degree atrioventricular (AV) block or evidence of acute or sub-acute myocardial infarction or ischemia. [Note: Subjects with MRI compatible pacemakers or bundle branch block (BBB) and a paced QTc (Fridericia) < 480 msec and a stable cardiac status may be enrolled after obtaining a cardiology consult. It must be determined by the consulting cardiologist that the subject's cardiac status is stable and does not pose a risk for participation in the trial.]

4. Prohibited Treatments and/or Therapies

   1. History of not tolerating treatment with riluzole for any reason
   2. Treatment with riluzole in the 30 days prior to screening and/or during the study; [with the exception of the switch group of SCA subjects].
   3. Prior trial of riluzole treatment of at least 8 weeks duration ; [with the exception of the switch group of SCA subjects].
   4. Use of chlorzoxazone is prohibited 30 days prior to screening and during the study;
   5. Use of aminopyridine is prohibited 30 days prior to screening and during the study;
   6. Use of tricyclic antidepressants and mono-amine-oxidase (MAO) inhibitors are prohibited 30 days prior to screening and during the study;
   7. Use of any approved treatments for Alzheimer's Disease (AD). Subjects should be free of such medications (donepezil, galantamine, rivastigmine and memantine) for at least 3 months prior to Baseline with no plans to start such medications during the study; or, subjects should be on stable doses of these medications for at least 3 months prior to the baseline visit;
   8. Use of memantine is prohibited 30 days prior to screening and during the study;
   9. A new anxiolytic or sleep medication not taken at a stable dose within 30 days prior to screening. Note: Low dose anxiolytic pre-medications prior to diagnostic testing (e.g., MRI) as well as sleep medications taken prn (as needed) are allowed;
   10. Chronic NSAID use (e.g., naproxen, acetylsalicylic acid, ibuprofen) should be treated with proton pump inhibitors unless otherwise clinically prohibited;
   11. Medical marijuana use within 30 days of baseline visit (and subjects will be expected to refrain from use during the period of the study).

The information will only be made available to the research team and the Sponsor, BioHaven Pharmaceuticals

This is an open trial. There is no masking.