We present high spatial resolution ( 1.2 ^ { \prime \prime } ) mm-interferometric observations of the ^ { 12 } CO ( 2 - 1 ) line emission in the central 300 \ > { pc } of the late-type spiral galaxy IC 342 . The data , obtained with the Owens Valley Radio Observatory , allow first-time detection of a molecular gas disk that coincides with the luminous young stellar cluster in the nucleus of IC 342 . The nuclear CO disk has a diameter of \sim 30 \ > { pc } and a molecular gas mass of M _ { H _ { 2 } } \sim 2 \times 10 ^ { 5 } \ > { M _ { \odot } } . It connects via two faint CO bridges to the well-known , 100 \ > { pc } diameter circumnuclear gas ring . Analysis of the gas kinematics shows that the line-of-nodes in the inner 15 \ > { pc } is offset by about 45 ^ { \circ } from the major kinematic axis , indicating non-circular motion of the gas within a few parsec of the dynamical center of IC 342 . Both the morphology and the kinematics of the CO gas indicate ongoing inflow of molecular gas into the central few parsec of IC 342 . We infer a gas inflow rate between 0.003 and 0.14 \ > \ > { M _ { \odot } } yr ^ { -1 } , based on the observed surface density of the nuclear gas disk and estimates of the radial velocities of the surrounding gas . Inflow rates of this order can support repetitive star formation events in the nucleus of IC 342 on timescales much smaller than a Hubble time .