We present high-resolution sub/millimeter interferometric imaging of the Class 0 protostar L1527 IRS (IRAS 04368+2557) at 870 micron and 3.4 mm from the Submillimeter Array (SMA) and Combined Array for Research in Millimeter Astronomy (CARMA). We detect the signature of an edge-on disk surrounding the protostar with an observed diameter of 180 AU in the sub/millimeter images. The mass of the disk is estimated to be 0.007 M_sun, assuming optically thin, isothermal dust emission. The millimeter spectral index is observed to be quite shallow at all the spatial scales probed; alpha ~ 2, implying a dust opacity spectral index beta ~ 0. We model the emission from the disk and surrounding envelope using Monte Carlo radiative transfer codes, simultaneously fitting the sub/millimeter visibility amplitudes, sub/millimeter images, resolved Larcmin image, spectral energy distribution, and mid-infrared spectrum. The best fitting model has a disk radius of R = 125 AU, is highly flared (H ~ R^1.3), has a radial density profile rho ~ R^-2.5, and has a mass of 0.0075 M_sun. The scale height at 100 AU is 48 AU, about a factor of two greater than vertical hydrostatic equilibrium. The resolved millimeter observations indicate that disks may grow rapidly throughout the Class 0 phase. The mass and radius of the young disk around L1527 is comparable to disks around pre-main sequence stars; however, the disk is considerably more vertically extended, possibly due to a combination of lower protostellar mass, infall onto the disk upper layers, and little settling of ~1 micron-sized dust grains.
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