Testing varenicline to reduce falls

Inclusion Criteria: * Participants with a PD diagnosis based on the Movement Disorders Society Clinical Diagnostic Criteria for Parkinson's Disease at the time of baseline screening/enrollment visit * Participants with occipital association cortex cholinergic denervation in the lowest tertile of the normal range on F-fluoroethoxybenzovesamicol (FEOBV) Positron Emission Tomography (PET) * Participants with legally authorized representatives (LARs) able to co-sign documented informed consent or participants that have capacity to provide informed consent upon study enrollment as ascertained by the study-specific University of California, San Diego Brief Assessment of Capacity to Consent (UBACC) * Mild Cognitive Impairment consistent with Parkinson disease Mild Cognitive Impairment (PD-MCI) Exclusion Criteria: * Atypical Parkinsonian conditions other than Parkinson disease (PD) * Participants initially on certain dopamine blocking drugs (per protocol), specific anticholinergic drugs (trihexyphenidyl, benztropine), or specific cholinesterase inhibitor drugs (per protocol) at the in-person screening visit * Modified Hoehn and Yahr score of 4.0 or greater at the in-person screening visit * Current or previous (within last 6 months of in-person screening visit) use of any product or medication containing nicotinic agents, including use of tobacco products such as cigarettes, cigars, pipes, chewing tobacco, etc., e-cigarettes, over the counter (OTC) nicotine patches, chewing gum containing nicotine, or varenicline * Evidence of a stroke with both cortical and subcortical involvement or occipital lobe mass lesion on structural magnetic brain imaging (MRI) obtained at the in-person screening visit that would preclude co-registration and analysis of FEOBV PET data * Participants where magnetic resonance imaging (MRI) is contraindicated including, but not limited to, those with a pacemaker, presence of metallic fragments near the eyes or spinal cord, or cochlear implant * Severe claustrophobia precluding MRI or PET imaging * Participants limited by participation in research procedures involving ionizing radiation * Pregnancy (test within 48 hours of the PET imaging session in women of childbearing potential) or breastfeeding at the time of in-person screening visit * Participants with stage 4 or 5 chronic kidney disease at the time of in-person screening visit (estimated Creatinine Clearance \< 30 milliliters per minute) * Current, significant mood disorder at the time of in-person screening/enrollment visit defined as follows: persistent (lasting longer than 2 weeks) symptoms of depression or anxiety in the 30 days preceding informed consent, as determined by self-report * Evidence of active suicidal ideation as defined by an affirmative answer to either question 1 or 2 on the Columbia Suicide Severity Rating Scale (C-SSRS) * History of a myocardial infarction or unstable angina in the 90 days preceding enrollment visit * A current or previous history of epilepsy or any epileptic seizures in the 12 months preceding enrollment * Heavy alcohol use as defined by a score of 8 or greater on the Alcohol Use Disorders Identification Test (AUDIT-self-report version) at the time of screening/enrollment visit * Participants that are unable to swallow pills * Participants with a history of allergic reaction to varenicline * Participants that are actively taking part in another ongoing interventional (i.e., not observational) clinical trial