The origin of the fundamental crustal dichotomy on Mars remains the outstanding unsolved problem in martian geologic evolution. The hypothesis that this dichotomy is due to a single giant (mega) impact early in martian history is tested by comparing the observed number of large impact basins on Mars with the number expected from a D-2 distribution. This test is based on the assumption that the mega-impact Borealis Basin is the largest member of such a distribution. The difference between observed and ''expected'' basins is the number of ''missing'' basins that might have been obscured by subsequent geologic events. If the Borealis Basin were the largest member of a D-2 impact population, there would be a very large number of ''missing'' basins on Mars: 1 larger than 5000 km, 10 larger than 2000 km and 40--50 larger than about 1000 km diameter. The area occupied by these ''missing'' basins (allowing for overlap) is too large to be hidden by the younger surface units. A large population of presently unrecognized large impact basins would have to be located in the well preserved cratered highlands. By contrast, if Chryse is the largest member of a D-2 impact population, the more modest number of ''missing'' basins could in principle be confined to areas of Mars that have been resurfaced or reworked by subsequent geologic processes. A possible alternative to the mega-impact hypothesis is that the crustal dichotomy is due to the cumulative effects of multiple overlapping large (but not giant) impacts. ¿ American Geophysical Union 1988