We construct supersymmetric AdS_{3}×Σ solutions of minimal gauged supergravity in D=5, where Σ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on S^{5}, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to d=2, N=(0,2) SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on Σ.