We present a simple statistical model of molecular function evolution to predict protein function. The model description encodes general knowledge of how molecular function evolves within a phylogenetic tree based on the proteins' sequence. Inputs are a phylogeny for a set of evolutionarily related protein sequences and any available function characterizations for those proteins. Posterior probabilities for each protein are used to predict the molecular function of that protein. We present results from applying our model to three protein families, and compare our prediction results on the extant proteins to other available protein function prediction methods. For the deaminase family, our method achieves 93.9% where related methods BLAST achieves 72.7%, GOtcha achieves 87.9%, and Orthostrapper achieves 72.7% in prediction accuracy.