  We construct a supersymmetric extension of double field theory that realizes
the ten-dimensional Majorana-Weyl local supersymmetry. In terms of a stringy
differential geometry we proposed earlier, our action consists of five simple
terms -- two bosonic plus three fermionic -- and manifests not only
diffeomorphism and one-form gauge symmetry of B-field, but also O(10,10)
T-duality as well as a direct product of two local Lorentz symmetries, SO(1,9)
\times SO(9,1). A gauge fixing that identifies the double local Lorentz groups
reduces our action to the minimal supergravity in ten dimensions.
