  We present affine Lie algebras generated by the supercovariant derivatives
and the supersymmetry generators for the left and right moving modes in the
doubled space. Chirality is manifest in our doubled space as well as the
T-duality symmetry. We present gauge invariant bosonic and superstring actions
preserving the two-dimensional diffeomorphism invariance and the kappa-symmetry
where doubled spacetime coordinates are chiral fields. The doubled space
becomes the usual space by dimensional reduction constraints.
