This paper presents the results of an analysis of indicators that can be used to predict whether a student will succeed in a Computer Science Ph.D. program. The analysis was conducted by studying the records of 75 students who have been in the Computer Science Ph.D. program of the University of Alabama in Huntsville. Seventy-seven variables were extracted from each student's record, and the variables were correlated with whether the student did or did not successfully graduate from the program. A multivariate model was developed that predicts success with a high degree of accuracy. Importantly, the model relies on variables that can be determined reasonably early in a student's Ph.D. class work, enabling its use as a selection metric. Hypotheses about the composition of the model are also presented and discussed.