We present a new class of solutions of D = 10, N = 2 chiral supergravity. A non-vanishing background for the field strength G_MNR of the complex two-form triggers AdS₃ × M₇ compactifications, where M₇ is a 7-dimensional compact manifold. When M₇ is a non-symmetric coset space G/H, we can always find a set of constants G_MNR covariantly conserved and thus satisfying the field equations. For example the structure constants of G with indices in the G/H directions are a covariantly conserved tensor. In some symmetric G/H, where these structure constants vanish, there may still exist conserved 3-forms, yielding AdS₃ × G/H solutions. The conditions for supersymmetry of the AdS₃ × M₇ compactifications are derived, and tested for the supersymmetric solutions AdS₃ × S³ × ⁴ and AdS₃ × S³ × S³ × S¹. Finally, we show that the AdS₃ × S³ × ⁴ supersymmetric background can be seen as the σ = 0 limit in a one-parameter class of solutions of the form AdS₃ × S³ × ², the parameter σ being the inverse ``radius" of ². For σ≠0 all supersymmetries are broken.