We provide maximum likelihood estimators of term structures of conditional probabilities of corporate default, incorporating the dynamics of firm-specific and macroeconomic covariates. For U.S. Industrial firms, based on over 390,000 firm-months of data spanning 1979 to 2004, the level and shape of the estimated term structure of conditional future default probabilities depends on a firm's distance to default (a volatility-adjusted measure of leverage), on the firm's trailing stock return, on trailing S & P 500 returns, and on U.S. interest rates, among other covariates. Variation in a firm's distance to default has a substantially greater effect on the term structure of future default hazard rates than does a comparatively significant change in any of the other covariates. Default intensities are estimated to be lower with higher short-term interest rates. The out-of-sample predictive performance of the model is an improvement over that of other available models.