This article develops a semiparametric, minimum chi-squared estimation method of the proportional hazard model for the case when durations are grouped and covariates are categorical. The proposed estimator is easy to compute, yet asymptotically as efficient as the maximum likelihood estimator. This article also suggests simple specification tests for the proportional hazard model. If proportionality holds, then two sets of minimum chi-squared estimators, one from a further grouped data and the other from the original grouped data, will converge to the same quantity; otherwise, they will not. Therefore, a test of the equality of these two sets of estimators will offer a test for proportionality. Monte Carlo simulations demonstrate the performance of these estimators and specification tests. In addition, two real data applications illustrate the implementation of the suggested methods and the contexts in which these methods are useful.