We present ∼0 4 resolution images of CO(3-2) and associated continuum emission from the gas-bearing debris disk around the nearby A star 49 Ceti, observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). We analyze the ALMA visibilities in tandem with the broadband spectral energy distribution to measure the radial surface density profiles of dust and gas emission from the system. The dust surface density decreases with radius between ∼100 and 310 au, with a marginally significant enhancement of surface density at a radius of ∼110 au. The SED requires an inner disk of small grains in addition to the outer disk of larger grains resolved by ALMA. The gas disk exhibits a surface density profile that increases with radius, contrary to most previous spatially resolved observations of circumstellar gas disks. While ∼80% of the CO flux is well described by an axisymmetric power-law disk in Keplerian rotation about the central star, residuals at ∼20% of the peak flux exhibit a departure from axisymmetry suggestive of spiral arms or a warp in the gas disk. The radial extent of the gas disk (∼220 au) is smaller than that of the dust disk (∼300 au), consistent with recent observations of other gasbearing debris disks. While there are so far only three broad debris disks with wellcharacterized radial dust profiles at millimeter wavelengths, 49 Ceti's disk shows a markedly different structure from two radially resolved gas-poor debris disks, implying that the physical processes generating and sculpting the gas and dust are fundamentally different.