The objective of the study is to determine if treatment with Ramelteon will help to improve insomnia in older adults with co-existent insomnia and sleep apnea. The primary study objective is sleep latency (a measure of insomnia). The hypothesis is that sleep latency will be reduced in subjects taking Ramelteon relative to the placebo arm. The secondary study objective is to determine if subject compliance with CPAP treatment of their sleep apnea is improved in subjects taking Ramelteon (their compliance may be improved because they would have less insomnia due to Ramelteon treatment when using their CPAP). The hypothesis is that compliance with CPAP will be improved in subjects taking Ramelteon relative to the placebo arm.