The ACS Survey of Galactic globular clusters is a Hubble Space Telescope Treasury program designed to provide a new large, deep, and homogeneous photometric database. Based on observations from this program, we have measured precise relative ages for a sample of 64 Galactic globular clusters by comparing the relative position of the clusters' main-sequence (MS) turnoffs, using MS fitting to cross-compare clusters within the sample. This method provides relative ages to a formal precision of 2%-7%. We demonstrate that the calculated relative ages are independent of the choice of theoretical model. We find that the Galactic globular cluster sample can be divided into two groups—a population of old clusters with an age dispersion of ~5% and no age-metallicity relation, and a group of younger clusters with an age-metallicity relation similar to that of the globular clusters associated with the Sagittarius dwarf galaxy. These results are consistent with the Milky Way halo having formed in two phases or processes. The first one would be compatible with a rapid (<0.8 Gyr) assembling process of the halo, in which the clusters in the old group were formed. Also these clusters could have been formed before re-ionization in dwarf galaxies that would later merge to build the Milky Way halo as predicted by ΛCDM cosmology. However, the galactocentric metallicity gradient shown by these clusters seems difficult to reconcile with the latter. As for the younger clusters, it is very tempting to argue that their origin is related to their formation within Milky Way satellite galaxies that were later accreted, but the origin of the age-metallicity relation remains unclear.