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In cell differentiation, a cell of a less specialized type becomes one of a more specialized type, even though all cells have the same genome. Transcription factors and epigenetic marks like histone modifications can play a significant role in the differentiation process. In this paper, we present a simple analysis of cell types and differentiation paths using phylogenetic inference based on ChIP-Seq histone modification data. We propose new data representation techniques and new distance measures for ChIP-Seq data and use these together with standard phylogenetic inference methods to build biologically meaningful trees that indicate how diverse types of cells are related. We demonstrate our approach on H3K4me3 and H3K27me3 data for 37 and 13 types of cells respectively, using the dataset to explore various issues surrounding replicate data, variability between cells of the same type, and robustness. The promising results we obtain point the way to a new approach to the study of cell differentiation., Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013)