  We construct the N=1 supersymmetric extension of double field theory for
D=10, including the coupling to an arbitrary number n of abelian vector
multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space
symmetry under which the fermions transform. It is shown that the supersymmetry
transformations close into the generalized diffeomorphisms of double field
theory.
