Heart failure affects approximately 5-6 million North Americans and is increasing in prevalence. Sleep-related disorders, such as obstructive sleep apnea (OSA) often coexist (11-37% incidence) with heart failure. OSA is the repeated temporary interruption of breathing during sleep and occurs when the air passages in the upper respiratory tract become blocked during sleep. OSA adversely affects the cardiovascular system resulting in hypoxia (decrease in oxygen supply), which decreases the oxygen supply to the heart. Patients with OSA are treated with continuous positive airway pressure (CPAP). It has also been shown that CPAP reduces angina during sleep, minimizes sympathetic nervous system (SNS) activation and improves left ventricular (LV) function, although the mechanism of action is not clear. Carbon-11 acetate PET imaging allows for the assessment of how the heart works and how efficiently the heart uses oxygen in certain circumstances. Carbon-11 hydroxyephedrine (HED) measures cardiac nervous system activity, which may have an effect on heart rate. The study will evaluate the term effects of continuous positive airway pressure (CPAP), a common treatment for patients with OSA, on the heart's efficiency or ability to work and its effect on the nervous system activity of the heart. Two patient groups will be evaluated 1.) patients with congestive heart failure and obstructive sleep apnea will be randomized to early or late CPAP to address the primary hypothesis of the study and 2.) patients with congestive heart failure only (matched control group). Both the primary randomized study group and secondary study group will be evaluated using [11C]acetate PET, [11C]HED PET and echocardiography. Measurements will be obtained at baseline, 1 week (where possible) and 6-8 weeks.