We present new optical observations of young massive star clusters in Arp 220 , the nearest ultraluminous infrared galaxy , taken in UBVI with the Hubble Space Telescope ACS/HRC camera . We find a total of 206 probable clusters whose spatial distribution is centrally concentrated toward the nucleus of Arp 220 . We use model star cluster tracks to determine ages , luminosities , and masses for 14 clusters with complete UBVI indices or previously published near-infrared data . We estimate rough masses for 24 additional clusters with I < 24 mag from BVI indices alone . The clusters with useful ages fall into two distinct groups : a “ young ” population ( < 10 Myr ) and an intermediate-age population ( \simeq 300 Myr ) . There are many clusters with masses clearly above 10 ^ { 6 } M _ { \odot } and possibly even above 10 ^ { 7 } M _ { \odot } in the most extreme instances . These masses are high enough that the clusters being formed in the Arp 220 starburst can be considered as genuine young globular clusters . In addition , this study allows us to extend the observed correlation between global star formation rate and maximum cluster luminosity by more than an order of magnitude in star formation rate .