The goal of this clinical trial is to evaluate if the investigational drug, RL-007, can improve the cognitive performance of subjects with schizophrenia. The main questions the study aims to answer are:

1. Does RL-007 improve subjects performance in a set of cognitive tasks?
2. Which dose of RL-007 (20 mg or 40 mg) has a larger effect on cognitive performance?
3. How well do subjects tolerate RL-007?

In the study, subjects will perform the cognitive tasks at the beginning to get familiar with the tasks. Then, subjects will be given either RL-007 or a placebo for 6 weeks and then repeat the cognitive tasks. The researchers will compare the results at the end of the treatment period to the baseline to see if there have been any changes in performance.

Additionally, several safety measures will be collected throughout the study (blood pressure, physical exam, ECGs, etc) to evaluate if there are any side effects from taking RL-007.

This is a randomized, 3-arm, placebo-controlled, double-blinded clinical trial to evaluate the efficacy, safety, and tolerability of RL-007 in subjects with stable schizophrenia. The treatment period is 6 weeks.

Key Inclusion Criteria:

• Diagnosis of schizophrenia, per Diagnostic and Statistical Manual (DSM) 5, with a duration of at least 6 months
• Positive and Negative Symptoms Severity Score (PANSS) of less than or equal to 80 (inclusive)
• Currently treated on a single atypical antipsychotic (other than clozapine) at a stable dose and clinically stable for at least 6 weeks before randomization
• Clinical Global Impression - Severity score < 5.
• Body mass index (BMI) <= 40.0 kg/m^2 at screening
• Participant has reliable housing that is not expected to change during the study period with no expected significant life events that could affect study outcomes throughout entire study period.
• Sufficient fluency in English to understand and complete study instructions and assessments

Key Exclusion Criteria:

• History of hospitalization for medical indication or psychiatric hospitalization within 3 months prior to screening.
• Participants who present a serious risk of suicide, as evidenced by a) "yes" on items 4 or 5 on the Columbia-Suicide Severity Rating Scale (C-SSRS) and meeting these criteria within the past 6 months, or b) posing a significant suicide risk in the Investigator's judgement.
• Participants who present a risk of serious harm to others, as evidence by any history within the past 2 years and any expressed homicidal ideation (with or without plan).
• Current diagnosis of another major psychiatric disorder, intellectual disability, or any major neurological disease, brain injury, epilepsy, or severe brain trauma.
• Evidence or history of significant cognitive impairment, other than associated with schizophrenia, that in the judgement of the Investigator or Sponsor would confound interpretation of study data or prevent safe and satisfactory completion of the study protocol.
• Meets criteria for moderate to severe substance/drug abuse disorder (including alcohol) per DSM-5 within the last 6 months prior to informed consent or a positive alcohol breath test or urine test for drugs of abuse at either Screening or Randomization Visits (except for benzodiazepines taken according to prescription and as an ongoing, stable regimen).
• Participant has undergone electroconvulsive therapy within the past 12 months.