String theory predicts its own gravity rather than GR. In General Relativity the metric is the only geometric and gravitational field, whereas in string theory the closed-string massless sector comprises a skew-symmetric B-field and the string dilaton in addition to the metric. Furthermore, these three fields transform into each other under T-duality. This hints at a natural augmentation of GR: upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into `Stringy Gravity'. Equipped with an O(D,D) covariant differential geometry beyond Riemann, we spell out the definitions of the stringy Einstein curvature tensor and the stringy Energy-Momentum tensor. Equating them, all the equations of motion of the closed string massless sector are unified into a single expression which we dub the Einstein Double Field Equations.