This study will comprise an 18-week open label safety and tolerability trial. In this study, a total of 35 subjects with primary lateral sclerosis PLS or upper motor neuron predominate ALS will be enrolled. At the initial screening evaluation, a baseline T25FW will be obtained. This baseline test will be repeated at weeks 2, 4, 6, 10, 14 18. The validity of this measure was shown in MS studies when compared to the MSWS-12 (12 item walking scale) and CGI (clinical global impression) scales (35-37). A consistent responder will be defined as improvement in 3 of 4 Timed 25Foot Walk while on medication, compared with the baseline results while off medication.

Inclusion Criteria:

1. Male or female, aged 18-99;
2. Diagnosis of upper motor neuron disease, compatible with PLS but may include upper motor neuron (UMN) predominant ALS, defined as only upper motor neuron (UMN) features in at least 2 body regions on examination.
3. EMG within 3 months of enrollment with minimal or no evidence of lower motor neuron disease,
4. Time from symptom onset > 18 months
5. No previous allergy to dalfampridine
6. No current or exposure to any therapeutic agent targeting PLS or ALS within 30 days of enrollment.
7. Must have a forced vital capacity (FVC) ≥ 60% of expected
8. Written informed consent prior to screening is present.
9. Subjects on a stable dose of or have not taken Riluzole for at least thirty days
10. Impaired walking as measured by a Hauser Index of greater than 1 and less than 7 (2 to 6, inclusive);
11. Mini Mental Status Score > 22 and deemed by the PI of being capable of providing informed consent and following trial procedures.
12. Geographically accessible to the site.
13. Women must not be able to become pregnant (e.g., post-menopausal, surgically sterile, or using adequate birth control methods) for the duration of the study and three months after study completion. Adequate contraception includes: abstinence, hormonal contraception (oral contraception, implanted contraception, injected contraception or other hormonal contraception, for example patch or contraceptive ring), intrauterine device (IUD) in place for ≥ 3 months, barrier method in conjunction with spermicide, or another adequate method.

Exclusion Criteria:

1. History of clinically significant liver disease, renal disease, peripheral neuropathy, serious peripheral vascular disease, known HSP or + C9orf72 or SPG4 mutation, or any other medical condition felt to be exclusionary by the investigator;
2. Unwillingness to sign informed consent or any other reasons for which the investigator feels the subject cannot complete the study;
3. Women who are pregnant, breastfeeding, or trying to become pregnant;
4. Active cancer within the previous 2 years, except treated basal cell carcinoma of the skin;
5. Subjects taking any other experimental drugs within 30 days prior to enrollment;
6. Patient has any history of seizures; brain surgery, brain implants, any metallic implants above the neck, cardiac pacemakers, cochlear implants, piercing or body modification above the neck, known history of TMS related complications or side-effects, tinnitus.
7. Patient has moderate or severe renal impairment as defined by a calculated creatinine clearance of ≤50 mL/minute;
8. Patient has been administered botulinum toxin in the lower extremities within 6 months prior to the screening visit and/or is expected to receive botulinum toxin in the lower extremities during the course of the study;
9. Patient has a known allergy to pyridine-containing substances or any of the inactive ingredients of the dalfampridine tablet (colloidal silicon dioxide, hydroxypropyl methylcellulose, magnesium stearate, microcrystalline cellulose, polyethylene glycol, and titanium dioxide);
10. Patient has a history of drug or alcohol abuse within the past year;
11. Patient has clinically significant abnormal laboratory values.
12. Anything else that, in the opinion of the SI, would place the subject at increased risk or preclude the subject's full compliance with or completion of the study.