We report the discovery of active star formation in the H I cloud associated with the interacting Seyfert system NGC 3227/3226 that was originally identified as a candidate tidal dwarf galaxy (TDG) by Mundell et al. and that we name J1023+1952. We present broadband optical B, R, I (from the Isaac Newton Telescope), and ultraviolet images (from XMM-Newton) that show that the H I cloud is associated with massive ongoing star formation seen as a cluster of blue knots (MB lesssim -15.5 mag) surrounded by a diffuse ultraviolet halo and cospatial with a ridge of high neutral hydrogen column density (NH ~ 3.7 × 1021 cm-2) in the southern half of the cloud. We also detect Hα emission from the knots with a flux density of FHα ~ 2.55 × 10-14 ergs s-1 cm-2 corresponding to a star formation rate of SFR(Hα) ~ 10.6 × 10-3 M☉ yr-1. J1023+1952 lies at the base of the northern tidal tail, and, although it spatially overlaps the edge of the disk of NGC 3227, Mundell et al. showed that the H I cloud is kinematically distinct with an H I mean velocity 150 km s-1 higher than that of NGC 3227. Comparison of ionized (Hα) and neutral (H I) gas kinematics of the cloud shows closely matched recessional velocities, providing strong evidence that the star-forming knots are embedded in J1023+1952 and are not merely optical knots in the background disk of NGC 3227, thus confirming J1023+1952 as a gas-rich (MH/LB > 1.5) dwarf galaxy. No star formation is detected in the northern half of the cloud, despite similar H I column densities; instead, our new high-resolution H I image shows a ridge of high column density coincident with the reddest structures evident in our B - I image. We suggest that these structures are caused by the background stellar continuum from the disk of NGC 3227 being absorbed by dust intrinsic to J1023+1952, thus placing J1023+1952 in front of NGC 3227 along the line of sight. We discuss two scenarios for the origin of J1023+1952: as a third, preexisting dwarf galaxy involved in the interaction with NGC 3227 and NGC 3226, or as a newly forming dwarf galaxy condensing out of the tidal debris removed from the gaseous disk of NGC 3227. The first scenario is feasible given that NGC 3227 is the brightest member of a galaxy group, an environment in which preexisting dwarf galaxies are expected to be common. However, the lack of a detectable old stellar population in J1023+1952 makes a tidal origin more likely. If J1023+1952 is a bound object forming from returning gaseous tidal tail material, its unusual location at the base of the northern tail implies a dynamically young age similar to its star formation age, and suggests it is in the earliest stages of TDG evolution. Whatever the origin of J1023+1952, we suggest that its star formation is shock-triggered by collapsing tidal debris.