There are few controlled studies that address whether treatment of sleep apnea improves glucose tolerance. This is a randomized, double-blind cross-over study of subjects with sleep apnea (apnea hypopnea index > 15) and impaired glucose tolerance. Subjects will be randomized to 8 weeks of Continuous Positive Airway Pressure (CPAP) or sham-CPAP, followed by the alternate therapy after a one month wash-out. After each treatment, subjects will undergo 2-hour oral glucose tolerance testing, polysomnography, actigraphy, and measurements of indices of glucose control. The investigators intend to analyze the changes in glucose metabolism and insulin sensitivity in patients with sleep apnea with CPAP intervention.