New Chandra X-ray data and extensive optical spectroscopy, obtained with AAOmega on the 3.9m Anglo-Australian Telescope, are used to study the complex merger taking place in the galaxy cluster Abell 2744. Combining our spectra with data from the literature provides a catalog of 1237 redshifts for extragalactic objects lying within 15' of the cluster center. From these, we confirm 343 cluster members projected within 3Mpc of the cluster center. Combining positions and velocities, we identify two major substructures, corresponding to the remnants of two major subclusters. The new data are consistent with a post-core-passage, major merger taking place along an axis that is tilted well out of the plane of the sky, together with an interloping minor merger. Supporting this interpretation, the new X-ray data reveal enriched, low entropy gas from the core of the approaching, major subcluster, lying ~2' north of the cluster center, and a shock front to the southeast of the previously known bright, compact core associated with the receding subcluster. The X-ray morphology of the compact core is consistent with a Bullet-like cluster viewed from within ~45{deg} of the merger axis. An X-ray peak ~3' northwest of the cluster center, with an associated cold front to the northeast and a trail of low entropy gas to the south, is interpreted as the remnant of an interloping minor merger taking place roughly in the plane of the sky. We infer approximate paths for the three merging components.