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We extend the proportional hazards model to a two-level model with a random intercept term and random coefficients. The parameters in the multilevel model are estimated by a combination of EM and Newton-Raphson algorithms. Even for samples of 50 groups, this method produces estimators of the fixed effects coefficients that are approximately unbiased and normally distributed. Two different methods, observed information and profile likelihood information, will be used to estimate the standard errors. This work is motivated by the goal of understanding the determinants of contraceptive use among Nepalese women in the Chitwan Valley Family Study (Axinn, Barber, and Chimire, 1997). We utilize a two-level hazard model to examine how education and access to education for children covary with the initiation of permanent contraceptive use.