This is a multicenter study to test the hypothesis that suvorexant (MK-4305) is superior to placebo in improving insomnia as measured by change from baseline in: subjective total sleep time and time to sleep onset, wake time after persistent sleep onset, and latency to onset of persistent sleep. Participants who complete the initial 3-month Treatment (TRT) Phase may participate in an optional 3-month Extension (EXT) Phase.