We present high-resolution (approximately 6") maps of the (CO)-C-13 emission in the nucleus of the nearby spiral galaxy Maffei 2 made with the Owens Valley Millimeter Interferometer. The optically thin (CO)-C-13 emission, a tracer of H-2 gas density, indicates that the molecular cloud distribution in the nucleus of Maffei 2 is remarkably well-correlated with the starburst as traced by radio continuum emission. Evidently the molecular density distribution determines the spatial structure of this starburst. The observed range of (CO)-C-13 emission implies H-2 column densities of N(H-2) = 0.13-1.3 x 10(32) cm-2, molecular surface densities of sigma-H-2 = 200-2000 M. pc-2, and visual extinctions of A(V) = 14-140 mag on size scales of approximately 150 pc. The molecular material forms a barlike structure 40" (1 kpc at an assumed distance of 5 Mpc) in extent, with a total H-2 mass of M(H-2) = 2.3 x 10(8) M.. Two dynamical components are evident in the (CO)-C-13 maps: a region within approximately 120 pc of the nucleus that appears to rotate rapidly as a solid body; then nearly Keplerian fall-off to a less-rapidly rotating region extending to a radius of approximately 500 pc. The most intense star formation activity appears in the inner solid body region of the rotation curve. Within the solid body region, gas accounts for approximately 40% of the estimated dynamical mass. The centroid of the molecular mass is offset by approximately 120 pc from the dynamical center of the galaxy. Since the dynamical time scale against winding by differential rotation is approximately 10(6) yr, some mechanism must contribute to the longevity of this nuclear bar structure, possibly spiral density waves.