The Carnegie-Chicago Hubble Program (CCHP) is re-calibrating the extragalactic SN Ia distance scale using exclusively Population II stars. This effort focuses on the Tip of the Red Giant Branch (TRGB) method, whose systematics are entirely independent of the Population I Cepheid-based determinations that have long served as calibrators for the SN Ia distance scale. We present deep Hubble Space Telescope imaging of the low surface-density and low line-of-sight reddening halos of two galaxies, NGC 1448 and NGC 1316, each of which have been hosts to recent SN Ia events. Provisionally anchoring the TRGB zero-point to the geometric distance to the Large Magellanic Cloud derived from detached eclipsing binaries, we measure extinction-corrected distance moduli of 31.23 +/-0.04 (stat) +/- 0.06 (sys) mag for NGC 1448 and 31.37 +/- 0.04 (stat) and +/- 0.06 (sys) mag for NGC 1316, respectively, giving metric distances of 17.7 +/- 0.3 (stat) +/- 0.5 (sys) Mpc, and 18.8 +/- 0.3 (stat) +/- 0.5 (sys) Mpc. We find agreement between our result and the available Cepheid distance for NGC 1448; for NGC 1316, where there are relatively few published distances based on direct measurements, we find that our result is consistent with the published SN Ia distances whose absolute scales are set from other locally-determined methods such as Cepheids. For NGC 1448 and NGC 1316, our distances are some of the most precise (and systematically accurate) measurements with errors at 1.7 (2.8) % and 1.6 (2.7) % levels, respectively.