We present the first metallicity gradient measurement for a grand-design face-on spiral galaxy at z ~ 1.5. This galaxy has been magnified by a factor of 22× by a massive, X-ray luminous galaxy cluster MACS J1149.5+2223 at z = 0.544. Using the Laser Guide Star Adaptive Optics aided integral field spectrograph OSIRIS on KECK II, we target the Hα emission and achieve a spatial resolution of 0farcs1, corresponding to a source-plane resolution of 170 pc. The galaxy has well-developed spiral arms and the nebular emission line dynamics clearly indicate a rotationally supported disk with V rot/σ ~ 4. The best-fit disk velocity field model yields a maximum rotation of V rotsin i = 150 ± 15 km s-1, and a dynamical mass of M dyn = (1.3 ± 0.2) × 1010 cosec2(i) M sun (within 2.5 kpc), where the inclination angle i = 45° ± 10°. Based on the [N II] and Hα ratios, we measured the radial chemical abundance gradient from the inner hundreds of parsecs out to ~5 kpc. The slope of the gradient is -0.16 ± 0.02 dex kpc-1, significantly steeper than the gradient of late-type or early-type galaxies in the local universe. If representative of disk galaxies at z ~ 1.5, our results support an "inside-out" disk formation scenario in which early infall/collapse in the galaxy center builds a chemically enriched nucleus, followed by slow enrichment of the disk over the next 9 Gyr.