Half of U.S. 50-year-olds will experience a nursing home stay before they die, and one in ten will incur out-of-pocket long-term care expenses in excess of $200,000. Surprisingly, only about 10% of individuals over age 62 have private long-term care insurance (LTCI) and LTCI takeup rates are low at all wealth levels. We analyze the contributions of Medicaid, administrative costs, and asymmetric information about nursing home entry risk to low LTCI takeup rates in a quantitative equilibrium contracting model. As in practice, the insurer in the model assigns individuals to risk groups based on noisy indicators of their nursing home entry risk. All individuals in frail and/or low-income risk groups are denied coverage because the cost of insuring any individual in these groups exceeds that individual's willingness-to-pay. Individuals in insurable risk groups are offered a menu of contracts whose terms vary across risk groups. We find that Medicaid accounts for low LTCI takeup rates of poorer individuals. However, administrative costs and adverse selection are responsible for low takeup rates of the rich. The model reproduces other empirical features of the LTCI market including the fact that owners of LTCI have about the same nursing home entry rates as non-owners.