  In this work, we study the supersymmetric warped conformal field theory in
two dimensions. We show that the Hofman-Strominger theorem on symmetry
enhancement could be generalized to the supersymmetric case. More precisely, we
find that within a chiral superspace $(x^+,\th)$, a two-dimensional field
theory with two translational invariance and a chiral scaling symmetry can have
enhanced local symmetry, under the assumption that the dilation spectrum is
discrete and non-negative. Similar to the pure bosonic case, there are two
kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field
theories, while the other being $N=1$ supersymmetric warped conformal field
theories (SWCFT). We study the properties of SWCFT, including the
representations of the algebra, the space of states and the correlation
functions of the superprimaries.
