  Chiral gauge theories in two dimensions with (0,2) supersymmetry admit a much
broader, and more interesting, class of vacuum solutions than their better
studied (2,2) counterparts. In this thesis, we will explore some of the
possibilities that are offered by this additional freedom by including
field-dependent theta-angles and FI parameters. The moduli spaces that will
result from this procedure correspond to heterotic string backgrounds with
non-trivial H-flux and NS-brane sources. Along the way, a remarkable
relationship between (0,2) gauge anomalies and H-flux will emerge.
