Planetary Camera images of peculiar galaxy Arp 220 taken with V, R, and I band filters reveal a very luminous object near the position of the western radio continuum source, assumed to be the major nucleus, and seven lesser objects within 2'' of this position. The most luminous object is formally coincident with the radio source to within the errors of HST pointing accuracy, but we have found an alternate, more compelling alignment of maps in which the eastern radio source coincides with one of the lesser objects and the OH radio sources reside near the surfaces of other optical objects. The proposed centering places the most luminous object 150 pc (0.4'') away from the western radio source. We explore the possibilities that the objects are either holes in the dense dust distribution, dusty clouds reflecting a hidden bright nucleus, or associations of bright young stars. We favor the interpretation that at least the brightest two objects are massive young star associations with luminosities 10(9)-10(11)L., but highly extinguished by intervening dust. These massive associations should fall into the nucleus on a time scale of 10(8) yr. About 10% of the enigmatic far-IR flux arises from the observed objects. In addition, if the diffuse starlight out to a radius of 8'' is dominated by stars with typical ages of order 108 yr (the time since the alleged merger of two galaxies), as is indicated by the blue colors at larger radius, then the lower limit to the reradiation of diffuse starlight contributes 3 x 10(11)L. to the far-infrared flux, or greater-than-or-equal-to 25% of the total far-IR flux. Three additional bright objects (M(V) almost-equal-to -13) located about 6'' from the core are likely young globular clusters, but any of these could be recently exploded supernovae instead. The expected supernovae rate, if the dominant energy source is young stars, is about one per month for the region where the intense far-infrared flux originates. Also, individual giant dust clouds are visible in these images. Their typical size is 300 pc (1'').