The stratigraphic distribution of fossil species contains potential information about phylogeny because some phylogenetic trees are more consistent with the distribution of fossils in the rock record than others. A maximum likelihood estimator of phylogeny is derived using an explicit mathematical model of fossil preservation. The method assumes that fossil preservations within lineages follow an independent Poisson process, but can be extended to include other preservation models. The performance of the method was examined using Monte Carlo simulation. The performance of the maximum likelihood estimator of topology increases with an increase in the preservation rate. The method is biased, like other methods of phylogeny estimation, when the rate of fossil preservation is low; estimated trees tend to be more asymmetrical than the true tree. The method appears to perform well as a tree rooting criterion even when preservation rates are low. We suggest several possible extensions of the method to address other questions about the nature of fossil preservation and the process of speciation and extinction over time and space.