Half of all stars reside in binary systems, many of which have orbital separations in excess of 1000 AU. Such binaries are typically identified in astrometric catalogs by matching the proper motions vectors of close stellar pairs. We present a fully Bayesian method that properly takes into account positions, proper motions, parallaxes, and their correlated uncertainties to identify widely ... [Show full abstract] separated stellar binaries. After applying our method to the >2 × 10 ⁶ stars in the Tycho-Gaia astrometric solution from Gaia DR1, we identify over 6000 candidate wide binaries. For those pairs with separations less than 40,000 AU, we determine the contamination rate to be ≈5%. This sample has an orbital separation ( a ) distribution that is roughly flat in log space for separations less than ~5000 AU and follows a power law of a−1.6 at larger separations.