  IC 1613 is an isolated dwarf galaxy within the Local Group. Low foreground
and internal extinction, low metallicity, and low crowding make it an
invaluable testbed for the calibration of the local distance ladder. We present
new, high-fidelity distance estimates to IC 1613 via its Tip of the Red Giant
Branch (TRGB) and its RR Lyrae (RRL) variables as part of the Carnegie-Chicago
Hubble Program, which seeks an alternate local route to \ho using Population II
stars. We have measured a TRGB magnitude I=20.35+/-0.01 (statistical)+/-0.01
(systematic) using wide-field observations obtained from the IMACS camera on
the Magellan-Baade telescope. We have further constructed optical and
near-infrared RRL light curves using archival BI- and new H- band observations
from the ACS/WFC and WFC3/IR instruments aboard the Hubble Space Telescope
(HST). In advance of future Gaia data releases, we set provisional values for
the TRGB luminosity via the Large Magellanic Cloud and Galactic RRL zero-points
via HST parallaxes. We find corresponding true distance moduli
\mu(TRGB)=24.30+/-0.03 (statistical)+/-0.05 (systematic) and
\mu(RRL)=24.28+/-0.04 (statistical+systematic). We compare our results to a
body of recent publications on IC 1613 and find no statistically significant
difference between the distances derived from stars of Population I and II.
