Inclusion Criteria:  Is able to provide voluntary, written informed consent. Has a current diagnosis of IH per International Classification of Sleep Disorders Second Edition (ICSD-2) or International Classification of Sleep Disorders Third Edition (ICSD-3) criteria. Male or female patient age ≥18 years at the time of Screening. Has an ESS score of ≥12 at Screening.  If on a treatment that could affect daytime sleepiness (including but not limited to sodium oxybate, stimulants, modafinil, and armodafinil):  Must be on a stable dose for at least 2 months prior to Screening and agree to continue the stable dose for the duration of the study. If not on a stable dose for 2 months prior to Screening, washout for 5 half-lives or 14 days, whichever is longer, prior to Day 1 and agree to remain off these treatments until completion of the study. Washout of tetrahydrocannabinol for 28 days prior to screening and agree to remain off for the duration of the study. A patient who is a female of child-bearing potential (FCBP) must have a negative serum pregnancy test at the Screening Visit and negative urine pregnancy test at the Baseline Visit (Visit 2) and at the end of the Stable Dose Period (Visit 4) and agree to remain abstinent or use an effective method of non-hormonal contraception to prevent pregnancy for the duration of the study and for 21 days after final dose of study drug. Must have a negative result on urine drug screen at the Screening Visit, Baseline Visit (Visit 2) and at the end of the Stable Dose Period (Visit 4). In the opinion of the Investigator, the patient is capable of understanding and complying with the protocol and administration of oral study drug.  Exclusion Criteria:  Has a current diagnosis of another sleep disorder (e.g., narcolepsy) except for managed obstructive sleep apnea (OSA). Has known unmanaged OSA or other hypoventilatory condition, e.g., has an Apnea Hypoxia Index (AHI) or Respiratory Disturbance Index (RDI) of ≥10 with or without bilevel positive airway pressure (BiPAP)/continuous positive airway pressure (CPAP) or other therapeutic management. Experiences a mean of <6 hours of sleep per night based on sleep diary during Screening (patients need to record at least 7 consecutive nights in their sleep diary within a 14-day period prior to the Baseline Visit [Visit 2]). Consistently consumes >600 mg of caffeine per day and is unable/unwilling to reduce caffeine intake to ≤600 mg per day for the duration of the study. Does not agree to discontinue any prohibited medication or substance listed in the protocol. Is currently using or has previously used pitolisant. Is currently breastfeeding or planning to breastfeed over the course of the study. Lactating women must agree not to breastfeed for the duration of the study and for 21 days after final dose of study drug. Participation in an interventional research study involving another investigational medication or device within 28 days or within 5 half-lives of the investigational medication (whichever is longer) prior to Screening. Has a primary diagnosis of a psychiatric illness that is not well controlled. Patients taking antidepressants who have not been on a stable dose of their antidepressant for at least 12 weeks prior to Screening; patients on a stable dose of their antidepressant for at least 12 weeks prior to Screening must agree to continue their stable dose for the duration of the study. Has a diagnosis of end-stage renal disease (ESRD) (estimated glomerular filtration rate [eGFR] of <15 mL/minute/1.73 m²) or severe hepatic impairment (Child-Pugh C). Has a diagnosis of moderate or severe renal impairment (eGFR ≥15 to ≤59 mL/minute/1.73 m²) or moderate hepatic impairment (Child-Pugh B) at Screening or at any time during the study. Has a history of long corrected QT interval (QTc) syndrome or corrected QT interval using Fridericia's formula (QTcF) >450 msec for males or >470 msec for females (QTcF = QT / 3√ RR) at Screening. Is receiving and is unable to discontinue a medication known to prolong the QT interval. Is receiving a concomitant medication that is known to be a strong cytochrome P450 (CYP) 2D6 inhibitor, a strong CYP3A4 inducer, or a centrally acting histamine 1 (H¹) receptor antagonist; patients who undergo a washout of these medications of at least 5 half-lives or one week (whichever is longer) may be enrolled in the study. Is a known CYP2D6 poor metabolizer (PM). Has abnormal laboratory values at Screening that are clinically significant as determined by the Investigator. Has initiated any new or change in allied health therapies or interventions that can interfere with the study outcomes within 28 days prior to Screening and at any time during the study, based on the Investigator's judgment. Has a current or recent (within 1 year) history of a substance use disorder or dependence disorder, including alcohol and caffeine use disorders as defined in the Diagnostic and Statistical Manual of Mental Disorders, 5th Edition (DSM-5). Has planned surgery during the study. Has a significant risk of committing suicide or suicidality based on history, routine psychiatric examination, Investigator's judgment, or who has an answer of "yes" on any question other than questions 1 to 3 on the Columbia-Suicide Severity Rating Scale (C-SSRS). Based on the judgment of the Investigator, is unsuitable for the study for any reason, including but not limited to an unstable or uncontrolled medical condition or one that might interfere with the conduct of the study, confound interpretation of study results, pose a health risk to the patient, or compromise the integrity of the study. This exclusion criterion applies not only to entry into the study, but also to continuation in the study, should such an unstable, uncontrolled, or serious medical condition arise.