Participants with Parkinson's disease and sleep apnea will take long-acting levodopa and placebo at bedtime for 2 weeks each, in a randomized order, with a 2-week washout period in-between. Sleep studies will be done at the end of each period. The primary outcome will be the apnea-hypopnea index change from baseline to on-medication, comparing active medication to placebo. Other outcomes will include other polysomnographic parameters such as oxygenation measures and sleep architecture variables, as well as the Epworth Sleepiness Scale, the Montreal Cognitive Assessment, the Parkinson's disease sleep scale and the Unified Parkinson's Disease Rating Scale. Adverse events will be closely monitored.