Half of U.S. 50-year-olds will experience a nursing home stay before they die, and a sizable fraction will incur out-of-pocket expenses in excess of$200,000. Surprisingly, only about 10 percent of individuals over age 62 have private long-term care insurance (LTCI), and many applicants are denied coverage by insurers because they are frail. This paper proposes an equilibrium optimal contracting framework that features demand-side frictions due to Medicaid and supply-side frictions due to adverse selection, market power and administrative costs of paying claims. We find that low LTCI take-up rates and rejections among poor individuals are due to Medicaid. Supply-side frictions, however, are responsible for rejections among frail affluent individuals, and both types of frictions matter for those in the middle class.