We present direct evidence of a collision of subclusters in the galaxy cluster Abell 754. Our comparison of new optical data and archival ROSAT PSPC X-ray data reveals three collision signatures predicted by n-body/hydrodynamical simulations of hierarchical cluster evolution. First, there is strong evidence of a nonhydrostatic process; neither of the two major clumps in the galaxy distribution lies on the off-center peak of the X-ray emission from the intracluster gas. Second, the peak of the X-ray emission is elongated perpendicular to the collision axis defined by connecting the centroids of the two galaxy clumps. Third, there is evidence of compression-heated gas; one of A754's two X-ray temperature components (Henry & Briel 1995) is among the hottest observed in any cluster and hotter than that inferred from the velocity dispersion of the associated galaxy clump. These signatures are consistent with the qualitative features of simulations (Evrard 1990a, b) in which two subclusters have collided in the plane of the sky during the last ~1 Gyr. The detection of such collisions is crucial for understanding both the dynamics of individual clusters and the underlying cosmology. First, for systems like A754, estimating the cluster X-ray mass from assumptions of hydrostatic equilibrium and isothermality is incorrect and may produce the discrepancies sometimes found between X-ray masses and those derived from gravitational lens models (Babul & Miralda-Escude 1994). Second, the fraction of nearby clusters in which subclusters have collided in the last ~1 Gyr is especially sensitive to the mean mass density parameter Omega 0 (see Richstone, Loeb, & Turner 1992; Evrard et al. 1993; Lacey & Cole 1993). As we show for A754, we now have the means to identify recent collisions. With a large, well-defined cluster sample, it will be possible to place a new and powerful constraint on cosmological models.