We have used Hα CCD imaging to map the distribution and intensity of massive star formation (MSF) in AM 0644-741, a large southern ring galaxy. MSF is restricted to a pair of interlocked 30 kpc diameter rings, with less than 1% contributed by a nuclear point source. Fifty percent of the total Hα emission originates in a crescent-shaped region defining the southwest quadrant of the most prominent ring (``A-ring''). North of the nucleus, MSF bifurcates into closely spaced rings of H II complexes. Particularly strong MSF occurs where they intersect. A broad continuum ring spans the disk south of the nucleus (``B-ring''). No diffuse MSF is found over the enclosed disk above an SFR per unit area of 0.15 M⊙ Gyr-1 pc-2 (3 σ), which is similar to limits set in the disks of S0 galaxies. However, low Hα surface brightness (ΣHα) complexes are found beyond the southwest A-ring. We derive a total Hα luminosity (LHα) of 3.0 × 1041 ergs s-1 (H0 = 100 km s-1 Mpc-1), and a total SFR of 3 M⊙ yr-1. Both values are significantly larger than those of field spirals and comparable to those found in interacting disk systems. The integrated Hα equivalent width (EWHα) is 14 Å, which is similar to values derived for noninteracting spirals. Systematic changes in LHα and EWHα with ring position angle were found in the A-ring, although much less pronounced than the Cartwheel's (Higdon 1995). Both A-rings and B-rings show only small azimuthal changes in red continuum. We have measured LHα and EWHα for 54 ring H II complexes. While their LHα tend to be higher than those commonly found in spiral galaxies, their EWHα are very similar. The H II luminosity function possesses a flat slope and large peak LHα, similar to those of irregular galaxies.We conclude that MSF in AM 0644-741 has been enhanced (~3×) and redistributed as a result of the intruder's passage and that the ring galaxy was originally an Sa-Sab spiral. We interpret the distribution of ΣHα around the rings and faint Hα emission beyond the southwest A-ring in terms of MSF triggered on the outer edge of a primarily gaseous ring density wave. We suggest that the unique double-ring structure reflects strong caustics along the inner and outer edges of a single-ring density wave. The much less extreme MSF properties in AM 0644 relative to the Cartwheel likely arise from a combination of a weaker orbit crowding in the ring, higher metallicity, and a thicker precollision disk. We compare our results with ring galaxy models, where we find mixed results: the basic distribution and kinematics of material in ring galaxies appear to be described reasonably well. However, recent models fail to reproduce the observed distribution of star forming regions.