Varying oral doses of Varenicline (VCN), starting with very low doses, will be administered to participants with Parkinson's Disease (PD) for several days. Positron emission tomography (PET) scans after administration of VCN will be used to determine the lowest oral dose of VCN producing an adequate brain level of VCN. With an appropriate oral dose of VCN identified, the investigators will administer VCN to PD participants to determine if VCN improves walking speed and measures of balance. VCN will receive VCN or a placebo (fake drug) for 3 weeks to assess the effects of VCN administration on gait speed and balance. Participants will undergo examinations to assess the intensity of their Parkinsonism and asked questions to assess their mood and thinking.