We report high-resolution (1A) imaging of CO (2È1) and dust continuum emission in the ultraluminous galaxy Arp 220. The CO (1È0) line was also imaged at 2A resolution for comparison. Both data sets recover essentially all of the observed single-dish line emission. Our aperture synthesis maps reveal for the Ðrst time, multiple components in the dense gas: peaks corresponding to each of the double nuclei (separated by 0A.95 at P.A.\101¡) seen in the near infrared and radio continuum and a more extended disklike structure at P.A.\53¡, similar to the dust lane seen in optical images. Approximately two-thirds of the total CO emission (and presumably the H mass) coincides with the compact double nucleus region. The ISM associated with these nuclear sour2ces is most apparent in the 1.3 mm dust continuum emission, but the brightest CO (2È1) emission is also correlated with the near infrared nuclei and exhibits a radial velocity di†erence of 250È300 km s~1 between the two nuclei. The latter is in excellent agreement with published near-infrared recombination line measurements. The observed velocity di†erence between the two nuclei is probably much less than their orbital velocity because the nuclei do not lie along the kinematic major axis of the inner disk. The elongated disk feature exhibits a monotonic velocity gradient parallel to the major axis of the CO intensity distribution with the highest receding velocities in the southwest and the highest approach velocities in the northeast. From the major/minor axis ratio (0.66), we infer that the disk is moderately inclined to the line of sight (i\40È50¡). Detailed modeling of the CO line proÐles using a Doppler image-deconvolution technique, analogous to Doppler radar imaging, yields a best-Ðt CO emissivity distribution and rotation curve which are mutually consistent in the sense that if the total mass distribution follows the CO emissivity, then it yields the derived rotation curve. The implied CO-to-H conversion ratio is 0.45 times the Galactic value if the bulk of the mass resides in the molecular gas, ra2ther than stars. This value is also consistent with that expected based on the likely molecular density and temperature in the nuclear disk of Arp 220. The total molecular gas mass for Arp 220 is D9]109 M with an uncertainty of D30% based on the line _ proÐle modeling. The peak gas surface density is D5.8]104 M pc~2 at 130 pc radius, while the two _ stellar nuclei are at D235 pc radius and at position angle midway between the major and minor axes of the gaseous disk. From the proÐle modeling we derive an intrinsic velocity dispersion in the disk of 90^20 km s~1 and thus a disk thickness (FWHM) of only 16 pc, assuming the disk is in hydrostatic equilibrium. With 5.4]109 M of molecular gas concentrated in the very thin disk associated with the _ twin nuclei, the mean density will be nH cm~3 (^30%), a value which is consistent with the 2^2]104 strong molecular emission from high dipole moment molecules such as HCN and HCO`. From the high brightness temperatures of the observed CO emission (17È21 K), we conclude that the area Ðlling factor of the disk is very high (^0.25) and therefore the gas must fairly uniformly Ðll the disk, rather than being in discrete self-gravitating clouds. This thin central disk will have inward accretion at ^100 M_ yr~1 due to viscous and spiral arm transfer of angular momentum. The line proÐles at the positions of the double nuclei are double peaked suggesting that there may also be less massive accretion disks associated with each nucleus. The fact that the bulk of the molecular gas has relaxed into a disk with large masses of gas concentrated interior to the double nuclei is consistent with scenarios in which the gas in merging systems settles into the center faster than the two stellar/starburst nuclei. We suggest that dense central accretion disks like that in Arp 220 may be a common feature in the evolution of ultraluminous starburst/AGN galaxies since similar qualitative features are seen in the molecular line data for other systems (e.g., Mrk 231 and NGC 6240).