The Carnegie-Chicago Hubble Program (CCHP) is undertaking a re-calibration of the extragalactic distance scale, using Type Ia supernovae that are tied to Tip of the Red Giant Branch (TRGB) distances to local galaxies. We present here deep Hubble Space Telescope (HST) ACS/WFC imaging of the resolved stellar populations in the metal-poor halos of the SN Ia host galaxies NGC 4424, NGC 4526, and NGC 4536. These three Virgo constellation galaxies are prime targets for calibrating the extragalactic distance scale given their relative proximity in the local Universe and their low line-of-sight reddenings. Anchoring the TRGB zero-point to the geometric distance to the Large Magellanic Cloud via detached eclipsing binaries, we measure extinction-corrected distance moduli of 31.00 +/- 0.03 (stat) +/- 0.06 (sys) mag, 30.98 +/- 0.03 (stat) +/- 0.06 (sys) mag, and 30.99 +/- 0.03 (stat) +/- 0.06 (sys) mag for NGC 4424, NGC 4526, and NGC 4536, respectively, or 15.8 +/- 0.2 (stat) +/- 0.4 (sys) Mpc, 15.7 +/- 0.2 (stat) +/- 0.4 (sys) Mpc, and 15.8 +/- 0.2 (stat) +/- 0.4 (sys) Mpc. For these three galaxies, the distances are the first based on the TRGB, and for NGC 4424 and NGC 4526, they are the highest precision distances published to date, each measured to 3%. Finally, we report good agreement between our TRGB distances and the available Cepheid distances for NGC 4424 and NGC 4536, demonstrating consistency between the distance scales currently derived from stars of Population I and II.
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