We present high-resolution sub/millimeter interferometric imaging of the Class 0 protostar L1527 IRS ( IRAS 04368+2557 ) at \lambda = 870 µm 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 \sim 2 , implying a dust opacity spectral index \beta \sim 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 ( H \propto R ^ { 1.3 } ) , has a radial density profile \rho \propto 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 \sim 1 µm-sized dust grains .