The ACS Survey of Galactic Globular Clusters is a Hubble Space Telescope (HST) 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 turn offs, using main-sequence 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 intrinsic age dispersion of ~3% 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. The first phase would be compatible with a rapid (<0.8 Gyr) assembling process of the halo, in which the clusters in the old group were formed. The second phase lasted much longer in time and resulted in a group of globular clusters with a clear age-metallicity relation. It is very tempting to argue that the origin of this second group of clusters is related to the accretion of Milky Way satellite galaxies, but the origin of the age-metallicity relation remains unclear.