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In this paper, we report on Chandra observations of the starburst galaxy NGC 922. NGC 922 is a drop-through ring galaxy with an expanding ring of star formation, similar in many respects to the Cartwheel galaxy. The Cartwheel galaxy is famous for hosting 12 ultraluminous X-ray sources (ULXs), most of which are in the star-forming ring. This is the largest number of ULXs seen in a single system and has led to speculation that the low metallicity of the Cartwheel (0.3 Z ☉) may optimize the conditions for ULX formation. In contrast, NGC 922 has metallicity near solar. The Chandra observations reveal a population of bright X-ray sources, including seven ULXs. The number of ULXs in NGC 922 and the Cartwheel scales with the star formation rate: we do not find any evidence for an excess of sources in the Cartwheel. Simulations of the binary population in these galaxies suggest that the ULX population in both systems is dominated by systems with strong wind accretion from supergiant donors onto direct-collapse black holes. The simulations correctly predict the ratio of the number of sources in NGC 922 and the Cartwheel. Thus, it would appear that the metallicity of the Cartwheel is not low enough to see a difference in the ULX population compared to NGC 922.