Rimegepant in Moderate Plaque-type Psoriasis

Inclusion Criteria: * Male or female patients with at least 3% body surface are involved with psoriasis and a PASI score \>5. * Between 18 and 75 years of age. * Documentation of a definite diagnosis of psoriasis by a dermatologist or biopsy. * For women of childbearing potential, a negative urine pregnancy test within 48 hours of randomization. Female subjects should not have attempted to become pregnant in the month prior to exposure to rimegepant and agree not to attempt to become pregnant for 8 weeks after exposure to rimegepant. * A valid form of contraception must be documented for men and women of child-bearing potential. * The two methods for women of childbearing potential should include: * One barrier method (for example, Diaphragm with spermicidal gel, condom with spermicidal gel, cervical caps or intrauterine devices placed for at least four weeks before sexual intercourse); AND * One additional method. The other method could include hormonal contraceptives, or second barrier method as listed above. * The two options for men of childbearing potential should include: * Simultaneous use of male condom, and for the female partner, hormonal contraceptives (for example, birth control pills, implants, patch, depot injection, used since at least 4 weeks) or intra-uterine contraceptive device (placed since at least 4 weeks) before sexual intercourse; OR simultaneous use of male condom, and for the female partner, diaphragm with intravaginally applied spermicide. Exclusion Criteria: * Any ongoing medical illness or condition that places the participant at higher risk for adverse outcomes or inability to complete study procedures in the opinion of the study investigator. * Pregnancy or breastfeeding. * Known autoimmune disorders other than psoriasis. * Current use of corticosteroids or immunosuppressive medications (for any reason). * Immunodeficiency diseases. * Use of any biologic agent/monoclonal antibody within 5 half-lifes prior to baseline. * Ultraviolet light treatment, cyclosporine, oral corticosteroids, methotrexate, oral retinoids, mycophenolate mofetil, thioguanine, hydroxyurea, sirolimus or azathioprine within the 4 weeks prior to baseline or had topical psoriasis treatment within the previous 2 weeks prior to baseline. * Participation in another clinical trial involving an investigational drug within the last 30 days prior to baseline. * Inability for woman of child-bearing potential to use an effective form of contraception if sexually active. * Use of any medication that is a strong or moderate inhibitor of CYP3A, a strong or moderate inducer of CYP3A, or an inhibitor of glycoprotein (P-gp) or Breast Cancer Resistance Protein (BCRP). Please see Section 7.8 for more information. * 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 6 months (24 weeks) prior to screening. * Uncontrolled hypertension or uncontrolled diabetes (however, subjects can be included who have stable hypertension and/or diabetes for 3 months (12 weeks) prior to screening). Blood pressure greater than 150 mm Hg systolic or 100 mm Hg diastolic after 10 minutes of rest is exclusionary * Subjects with an active episode of major depressive episode within the last 6 months are ineligible. Subjects with major depressive disorder or any anxiety disorder are eligible only if they are on stable medication for each disorder for at least 3 months prior to the Screening visit. * Subject has a history or diagnosis of Gilbert's Syndrome or any other active hepatic or biliary disorder * 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. * Subject has current diagnosis of major depressive disorder requiring treatment with atypical antipsychotics, schizophrenia, bipolar disorder, or borderline personality disorder. * History of gallstones. * Subject has current diagnosis of major depressive disorder requiring treatment with atypical antipsychotics, schizophrenia, bipolar disorder, or borderline personality disorder. * The use of CGRP antagonists (biologic \[e.g. Aimovig™, Emgality® and Ajovy™, VyeptiTM\] or small molecule \[ e.g. Ubrelvy™ {ubrogepant\]\]) other than rimegepant is prohibited during the study. * Concomitant use of atypical antipsychotics such as Abilify (aripiprazole), Zyprexa (olanzapine), Seroquel (quetiapine), Geodon (ziprasidone), or Risperdal (risperidone). * Depakote/Depakene (divalproex/valproic acid/valproate) is prohibited during the study. * Concomitant use of LAMICTAL (lamotrigine) is prohibited during the study. * Concomitant use of Modafinil (PROVIGIL®) is prohibited during the study. * Exclusionary screening lab test findings: * Serum bilirubin (Total, Direct or Indirect) \> 1 x ULN (Only abnormal values of between 1-1.5x ULN may be repeated once for assessment of eligibility prior to randomization) * AST or ALT \> 1 x ULN (Only abnormal values of between 1-1.5x ULN may be repeated once for assessment of eligibility prior to randomization) * Neutrophil count ≤ 1000/μL (or equivalent) * HbA1c \> 6.5%