We present high-resolution sub/millimeter interferometric imaging of the Class 0 protostar L1527 IRS (IRAS 04368 2557) at λ = 870 μm and 3.4 mm from the Submillimeter Array and Combined Array for Research in Millimeter Astronomy. 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 ⊙, assuming optically thin, isothermal dust emission. The millimeter spectral index is observed to be quite shallow at all the spatial scales probed: α ~ 2, implying a dust opacity spectral index β ~ 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 L' image, spectral energy distribution, and mid-infrared spectrum. The best-fitting model has a disk radius of R = 125 AU, is highly flared (HvpropR 1.3), has a radial density profile ρvpropR -2.5, and has a mass of 0.0075 M ⊙. 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 are 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 μm-sized dust grains.
