  The Carnegie-Chicago Hubble Program (CCHP) is building a direct path to the
Hubble constant (H0) using Population II stars as the calibrator of the SN
Ia-based distance scale. This path to calibrate the SN Ia is independent of the
systematics in the traditional Cepheid-based technique. In this paper, we
present the distance to M101, the host to SN2011fe, using the I-band tip of the
red giant branch (TRGB) based on observations from the ACS/WFC instrument on
the Hubble Space Telescope. The CCHP targets the halo of M101 where there is
little to no host-galaxy dust, the red giant branch is isolated from nearly all
other stellar populations, and there is virtually no source confusion or
crowding at the magnitude of the tip. Applying the standard procedure for the
TRGB method from the other works in the CCHP series, we find a
foreground-extinction-corrected M101 distance modulus of
{\mu_0}=29.07+/-0.04(stat)+/-0.05(sys) mag, which corresponds to a distance of
D=6.52+/-0.12(stat)+/-0.15(sys) Mpc. This result is consistent with several
recent Cepheid-based determinations, suggesting agreement between Population I
and II distance scales for this nearby SN Ia-host galaxy. We further analyze
four archival datasets for M101 that have targeted its outer disk to argue that
targeting in the stellar halo provides much more reliable distance measurements
from the TRGB method due to the combination of multiple structural components
and heavily population contamination. Application of the TRGB in complex
regions will have sources of uncertainty not accounted for in commonly used
uncertainty measurement techniques.
