The Carnegie-Chicago Hubble Program. III. The Distance to NGC 1365 via
  the Tip of the Red Giant Branch
  The Carnegie-Chicago Hubble Program seeks to anchor the distance scale of
Type Ia supernovae via the Tip of the Red Giant Branch (TRGB). Based on deep
$Hubble$ $Space$ $Telescope$ ACS/WFC imaging, we present an analysis of the
TRGB for the metal-poor halo of NGC 1365, a giant spiral galaxy in the Fornax
Cluster that is host to the supernova SN2012fr. We have measured its
extinction-corrected TRGB magnitude to be F814W $= 27.34 \pm 0.03_{stat}
\pm0.01_{sys}$ mag. In advance of future direct calibration by $Gaia$, we set a
provisional TRGB luminosity via the Large Magellanic Cloud and find a true
distance modulus $\mu_0 = 31.29 \pm 0.04_{stat}\pm0.05_{sys}$ mag or $D = 18.1
\pm 0.3_{stat} \pm0.4_{sys}$ Mpc. This high-fidelity measurement shows
excellent agreement with recent Cepheid-based distances to NGC 1365 and
suggests no significant difference in the distances derived from stars of
Population I and II. We revisit the error budget for the $CCHP$ path to the
Hubble Constant based on this analysis of one of our most distant hosts,
finding a 2.5% measurement is feasible with our current sample.
