The Smith Cloud is a gaseous high-velocity cloud (HVC) in an advanced state of accretion, only 2.9 kpc below the Galactic plane and due to impact the disk in 27 Myr. It is unique among HVCs in having a known distance (12.4+/-1.3 kpc) and a well-constrained 3D velocity (296 km/s), but its origin has long remained a mystery. Here we present the first absorption-line measurements of its metallicity, using HST/COS UV spectra of three AGN lying behind the Cloud together with Green Bank Telescope 21 cm spectra of the same directions. Using Voigt-profile fitting of the S II 1250, 1253, 1259 triplet together with ionization corrections derived from photoionization modeling, we derive the sulfur abundance in each direction; a weighted average of the three measurements gives [S/H]=-0.28+/-0.14, or 0.53+0.21-0.15 solar metallicity. The finding that the Smith Cloud is metal-enriched lends support to scenarios where it represents recycled Galactic material rather than the remnant of a dwarf galaxy or accreting intergalactic gas. The metallicity and trajectory of the Cloud are both indicative of an origin in the outer disk. However, its large mass and prograde kinematics remain to be fully explained. If the cloud has accreted cooling gas from the corona during its fountain trajectory, as predicted in recent theoretical work, its current mass would be higher than its launch mass, alleviating the mass concern.