Near-infrared images (lambda = 1.3-3.7-mu-m) are presented for the nuclear region of Arp 220. Color maps in J - H and H - K reveal steep gradients, and the two nuclei previously detected at 20 cm and 2.2-mu-m appear on the J - H image as peaks separated by 1". Hot dust emission (T is similar to 1000 K) at 3.7-mu-m and extremely red J - H and H - K colors are found for both nuclei. The increasingly red colors approaching the center of the galaxy are explained most naturally by a mixture of extinction and emission by increasing amounts of hot dust. The near-infrared emission is consistent with a circumnuclear starburst extending to a radius of almost-equal-to 1.5 kpc (4") from the nuclei; further from the center the colors are consistent with a normal late-type stellar population. Inside a radius of 1 kpc the color maps show a NE-SW elongation that aligns with the concentration of molecular gas seen in CO images. The SW portion of this region is coincident with a protrusion in radio continuum images, likely due to synchrotron emission from supernovae remnants with roughly the same spatial distribution as the hot dust. The observed 3.7-mu-m luminosity, when corrected for nuclear extinction determined by 10-mu-m silicate absorption measurements and normalized by the bolometric luminosity, is consistent with UV-excess quasars and is is similar to 10 times greater than that found in infrared luminous starburst galaxies. However, the observed nuclear K - L' color is not different from the nucleus of M82, so the current data cannot rule out a nuclear starburst as the dominant luminosity source. The images at lambda less-than-or-equal-to 2.2-mu-m do not completely reveal the underlying nuclei, which likely remain significantly obscured, even at 3.7-mu-m.