We present a measurement of the galaxy merger fraction and number density from observations in the Hubble Ultra Deep Field (HUDF) for 0.5 ≤ z ≤ 2.5. We fit the combination of broadband data and slitless spectroscopy of 1308 galaxies with stellar population synthesis models to select merging systems based on a stellar mass of ≥10¹⁰ M. When correcting for mass incompleteness, the major merger fraction is not simply proportional to (1 + z)^m but appears to peak at z_frac 1.3 ± 0.4. From this merger fraction, we infer that ~42% of massive galaxies have undergone a major merger since z 1. We show that the major merger number density peaks at z_dens 1.2, which marks the epoch where major merging of massive galaxies is most prevalent. This critical redshift is comparable to the peak of the cosmic star formation rate density and occurs roughly 2.6 Gyr earlier in cosmic time than the peak in the number density of the X-ray-selected active galactic nuclei. These observations support an indirect evolutionary link between merging, starburst, and active galaxies.