  The primary goal of the Carnegie Chicago Hubble Program (CCHP) is to
calibrate the zero-point of the Type Ia supernova (SN Ia) Hubble Diagram
through the use of Population II standard candles. So far, the CCHP has
measured direct distances to 11 SNe Ia, and here we increase that number to 15
with two new TRGB distances measured to NGC 5643 and NGC 1404, for a total of
20 SN Ia calibrators. We present resolved, point-source photometry from new
Hubble Space Telescope (HST) imaging of these two galaxies in the F814W and
F606W bandpasses. From each galaxy's stellar halo, we construct an F814W-band
luminosity function in which we detect an unambiguous edge feature identified
as the Tip of the Red Giant Branch (TRGB). For NGC 5643, we find $\mu_0 =
30.48\pm0.03(stat)\pm0.07(sys) $ mag, and for NGC 1404 we find $ \mu_0=31.36\pm
0.04(stat)\pm 0.05(sys)$ mag. From a preliminary consideration of the SNe Ia in
these galaxies, we find increased confidence in the results presented in Paper
VIII (Freedman et al. 2019). The high precision of our TRGB distances enables a
significant measurement of the 3D displacement between the Fornax Cluster
galaxies NGC 1404 and NGC 1316 (Fornax A) equal to $1.50^{+0.25}_{-0.39}$ Mpc,
which we show is in agreement with independent literature constraints.
