  We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma
model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear
sigma model these correspond to some of the holomorphic deformations of the
tangent bundle on the hypersurface. Combinatorial formulas are given for the
number of these deformations, and we show that these numbers are exchanged by
mirror symmetry in a subclass of the models.
