  M104 (NGC 4594; the Sombrero galaxy) is a nearby, well-studied elliptical
galaxy included in scores of surveys focused on understanding the details of
galaxy evolution. Despite the importance of observations of M104, a consensus
distance has not yet been established. Here, we use newly obtained Hubble Space
Telescope optical imaging to measure the distance to M104 based on the tip of
the red giant branch method. Our measurement yields the distance to M104 to be
9.55 +/- 0.13 +/- 0.31 Mpc equivalent to a distance modulus of 29.90 +/- 0.03
+/- 0.07 mag. Our distance is an improvement over previous results as we use a
well-calibrated, stable distance indicator, precision photometry in a optimally
selected field of view, and a Bayesian Maximum Likelihood technique that
reduces measurement uncertainties. The most discrepant previous results are due
to Tully-Fisher method distances, which are likely inappropriate for M104 given
its peculiar morphology and structure. Our results are part of a larger program
to measure accurate distances to a sample of well-known spiral galaxies
(including M51, M74, and M63) using the tip of the red giant branch method.
