  We compute the elliptic genera of two-dimensional N=(2,2) and N=(0,2) gauged
linear sigma models via supersymmetric localization, for rank-one gauge groups.
The elliptic genus is expressed as a sum over residues of a meromorphic
function whose argument is the holonomy of the gauge field along both the
spatial and the temporal directions of the torus. We illustrate our formulas by
a few examples including the quintic Calabi-Yau, N=(2,2) SU(2) and O(2) gauge
theories coupled to N fundamental chiral multiplets, and a geometric N=(0,2)
model.
