• Safety and tolerability (Incidence of treatment emergent adverse events) of BHV-3000 relative to placebo in patients with Trigeminal Neuralgia [ Time Frame: From Baseline to End of Randomization Phase up to 5 weeks. ]
  Safety and tolerability will be measured by the frequency and severity of adverse events and discontinuations due to adverse events.
• Efficacy of BHV-3000 vs placebo for improving physical function in Trigeminal Neuralgia patients as measured by the Penn Facial Pain Scale-Revised [ Time Frame: From Baseline to End of Randomization Phase ]
  12 questions in which the higher the score the more pain and disability
• Efficacy of BHV-3000 vs placebo for improving functional disability in Trigeminal Neuralgia patients as measured by the Pain Disability Index [ Time Frame: From Baseline to End of Randomization Phase, up to 5 weeks. ]
  7 question's that are Scored 0-10, ten being more disabled.
• Efficacy of BHV-3000 vs placebo on global functioning as measured by the Patient Global Impression of Change Scale. [ Time Frame: From Baseline to End of Randomization Phase, up to 5 weeks. ]
  Measured by a likert scale from No change to a great deal better.
• Efficacy of BHV-3000 vs placebo in providing symptomic pain relief as captured by daily rating of worst pain episode as measured by the 11 point numeric rating scale. [ Time Frame: From Baseline to End of Randomization Phase, up to 5 weeks. ]
  11 point numeric rating scale.

• Safety and tolerability of BHV-3000 relative to placebo in patients with Trigeminal Neuralgia [ Time Frame: From Baseline to End of Randomization Phaseup to 5 weeks. ]
  Safety and tolerability will be measured by the frequency and severity of adverse events and discontinuations due to adverse events
• Efficacy of BHV-3000 vs placebo for improving physical function in Trigeminal Neuralgia patients as measured by the Penn Facial Pain Scale-Revised [ Time Frame: From Baseline to End of Randomization Phase ]
• Efficacy of BHV-3000 vs placebo for improving functional disability in Trigeminal Neuralgia patients as measured by the Pain Disability Index [ Time Frame: From Baseline to End of Randomization Phase, up to 5 weeks. ]
• Efficacy of BHV-3000 vs placebo on global functioning as measured by the Patient Global Impression of Change Scale. [ Time Frame: From Baseline to End of Randomization Phase, up to 5 weeks. ]
• Efficacy of BHV-3000 vs placebo in improving emotional functioning as measured by the Hospital Anxiety and Depression Scale (HADS) [ Time Frame: From Randomization to end of treatment period, up to 5 weeks. ]
• Efficacy of BHV-3000 vs placebo in providing pain relief as captured by daily rating of worst pain episode as measured by the 11 point numeric rating scale. [ Time Frame: From Baseline to End of Randomization Phase, up to 5 weeks. ]

• Drug: Rimegepant
  BHV3000 (rimegepant) 75mg tablet
• Drug: Placebo
  Placebo

• Active Comparator: BHV3000
  Intervention: Drug: Rimegepant
• Placebo Comparator: Placebo
  Intervention: Drug: Placebo

Inclusion Criteria:

1. Subjects with a clinical diagnosis of typical or atypical classical trigeminal neuralgia based on the International Classification of Headache Disorders, 3rd edition, beta version.
2. Trigeminal neuralgia symptoms for a minimum of 8 weeks prior to randomization visit.
3. Neuroimaging to exclude another cause for the neuralgia, other than neurovascular compression.

Exclusion Criteria:

1. Subject has a structural lesion on neuroimaging, other than vascular compression of the trigeminal nerve or nerve root that would explain the neuralgia
2. Subject has a clinically evident neurologic deficit on neurologic exam of the cranial nerves
3. Subjects with a history of HIV disease
4. Subject history with current evidence of uncontrolled, unstable or recently diagnosed cardiovascular disease, such as ischemic heart disease, coronary artery vasospasm, and cerebral ischemia. Subjects with Myocardial Infarction (MI), Acute Coronary Syndrome (ACS), Percutaneous Coronary Intervention (PCI), cardiac surgery, stroke or transient ischemic attack (TIA) during the 6 months prior to screening
5. Uncontrolled hypertension (high blood pressure) at screening
6. Subject has a current diagnosis of major depression, other pain syndromes, psychiatric conditions (e.g., schizophrenia), dementia, or significant neurological disorders (other than migraine) that, in the Investigator's opinion, might interfere with study assessments
7. Subject has a history of gastric, or small intestinal surgery (including Gastric Bypass, Gastric Banding, Gastric Sleeve, Gastric Balloon, etc.), or has a disease that causes malabsorption
8. Subject has a history or diagnosis of Gilbert's Syndrome or any other active hepatic or biliary disorder
9. The subject has a history or current evidence of any significant and/or unstable medical conditions (e.g., history of congenital heart disease or arrhythmia, known suspected infection, hepatitis B or C, or cancer) that, in the investigator's opinion, would expose them to undue risk of a significant adverse event (AE) or interfere with assessments of safety or efficacy during the course of the trial
10. History of, treatment for, or evidence of, alcohol or drug abuse within the past 12 months or subjects who have met DSM-V criteria for any significant substance use disorder within the past 12 months from the date of the screening visit
11. Hematologic or solid malignancy diagnosis within 5 years prior to screening. Subjects with a history of localized basal cell or squamous cell skin cancer are eligible for the study if they are cancer-free prior to the screening visit in this study.
12. Hematologic or solid malignancy diagnosis within 5 years prior to screening. Subjects with a history of localized basal cell or squamous cell skin cancer are eligible for the study if they are cancer-free prior to the screening visit in this study.
13. Body mass index >33kg/m²
14. History of gallstones or cholecystectomy