The investigators propose a multi-site parallel group, randomized, double-blind, placebo-controlled Phase IV clinical trial to test the efficacy and safety of suvorexant on trauma-related sleep disturbance and PTSD symptoms in Veterans. The investigators will use a flexible dose design of suvorexant with a 2-week titration followed by a 10-week steady-dose phase. The investigators predict that suvorexant, as compared to placebo, will result in a greater decrease in insomnia on the Insomnia Severity Index (ISI) over the 12-week trial. The investigators also predict that suvorexant, as compared to placebo, will result in a greater reduction in non-sleep PTSD symptoms in the Clinician Administered PTSD Scale for Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSMV) (CAPS-5) over the 12-week trial. Secondarily, the investigators will examine potential objectively measured wrist actigraphy as a biological mechanism of clinical improvement with as well as concomitant effects on PTSD-related nightmares using the Pittsburgh Sleep Quality Index-PTSD addendum (PSQI-A). Pending a significant effect of suvorexant on PTSD, the investigators will perform exploratory analyses to evaluate whether sleep improvement mediates the effect of suvorexant on PTSD symptoms. The investigators will also examine safety and tolerability of suvorexant compared to placebo (including depression, mood, vigor, suicidality, and daytime somnolence, psychomotor vigilance, and functional disability). Results from this study will provide substantive rationale for the use of Suvorexant in the treatment of Veterans with these concerns. This study will be the first to examine a selective orexin-receptor antagonist in a Veteran sample with PTSD. Suvorexant is an accessible, non-stigmatized medication whose use and safety has been well-established in non-mental-health settings. It has outstanding promise for treating common and distressing symptoms in Veterans as well as civilians with trauma-related sleep disturbance and PTSD.