Super star clusters--extremely massive clusters found predominately in starburst environments--are essential building blocks in the formation of galaxies and thought to dominate star formation in the high-redshift universe. However, the transformation from molecular gas into these ultracompact star clusters is not well understood. To study this process, we used the Submillimeter Array and the Plateau de Bure Interferometer to obtain high angular resolution (~1.5" or 160pc) images of the Antennae overlap region in CO(2-1) to search for the molecular progenitors of the super star clusters. We resolve the molecular gas distribution into a large number of clouds, extending the differential cloud mass function down to a 5{sigma} completeness limit of 3.8x10^5^M_{sun}_. We identify a distinct break in the mass function around log M_mol_/M_{sun}_{approx}6.5, which separates the molecular clouds into two distinct populations. The smaller, less massive clouds reside in more quiescent areas in the region, while the larger, more massive clouds cluster around regions of intense star formation. A broken power-law fit to the mass function yields slopes of {alpha}=-1.39+/-0.10 and {alpha}=-1.44+/-0.14 for the low- and high-mass cloud population, well matched to the mass function found for super star clusters in the Antennae galaxies. We find large velocity gradients and velocity dispersions at the locations of intense star formation, suggestive of compressive shocks. It is likely that these environmental factors contribute to the formation of the observed massive molecular clouds and super star clusters in the Antennae galaxies.