The Antennae galaxies are the closest example of an ongoing major galaxy merger and, as such, represent a unique laboratory for furthering the understanding of the formation of exotic objects (e.g., tidal dwarf galaxies, ultraluminous X-ray sources, super stellar clusters). In a previous paper HST WFPC2 observations were used to demonstrate that the Antennae system might be at a distance considerably less than that conventionally assumed in the literature. Here we report new, much deeper HST ACS imaging that resolves the composite stellar populations and, most importantly, reveals a well-defined red giant branch. The tip of this red giant branch (TRGB) is unambiguously detected at I0TRGB = 26.65 ± 0.09 mag. Adopting the most recent calibration of the luminosity of the TRGB then yields a distance modulus for the Antennae of (mM)0 = 30.62 ± 0.17 corresponding to a distance of 13.3 ± 1.0 Mpc. This is consistent with our earlier result, once the different calibrations for the standard candle are considered. We briefly discuss the implications of this now well-determined shorter distance.