We present multiwavelength observations of the brightest galaxies in four X-ray-luminous groups at z ~ 0.37 that will merge to form a cluster comparable in mass to Coma. Ordered by increasing stellar mass, the four brightest group galaxies (BGGs) present a time sequence where BGG-1, 2, and 3 are in merging systems and BGG-4 is a massive remnant (M* = 6.7 × 1011 Msun). BGG-1 and 2 have bright, gravitationally bound companions and BGG-3 has two nuclei separated by only 2.5 kpc; thus, merging at z < 0.5 increases the BGG mass by gtrsim40% (tMGR < 2 Gyr) and V-band luminosity by ~0.4 mag. The BGGs' rest-frame (B − V) colors correspond to stellar ages of >3 Gyr, and their tight scatter in (B − V) color (σBV = 0.032) confirms that they formed the bulk of their stars at z > 0.9. Optical spectroscopy shows no signs of recent (< 1.5 Gyr) or ongoing star formation. Only two BGGs are weakly detected at 24 μm, and X-ray and optical data indicate that the emission in BGG-2 is due to an AGN. All four BGGs and their companions are early-type (bulge-dominated) galaxies, and they are embedded in diffuse stellar envelopes up to ~140 kpc across. The four BGG systems must evolve into the massive, red, early-type galaxies dominating local clusters. Our results show that (1) massive galaxies in groups and clusters form via dissipationless merging and (2) the group environment is critical for this process.