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Topological insulators (TIs) in the Bi _2 Se _3 family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band gap of Bi _2 Se _3 and Bi _2 Te _3 , localized at one-dimensional step edges. Here numerical simulations of a TI surface are used to explore the phenomenology of edge state formation at the single-quintuple layer step defects found ubiquitously on these materials. The modeled one-dimensional edge states are found to exhibit a stable topological connection to the two-dimensional surface state Dirac point.