  We construct new heterotic string backgrounds which are analogous to
superstring solutions corresponding to coset models but are not simply the
`embeddings'of the latter. They are described by the (1,0) supersymmetric
extension of the $G/H$ chiral gauged WZNW models. The `chiral gauged' WZNW
action differs from the standard gauged WZNW action by the absence of the
$A\bar A$-term (and thus is not gauge invariant in the usual sense) but can
still be expressed as a combination of WZNW actions and is conformal invariant.
We explain a close relation between gauged and chiral gauged WZNW models and
prove that in the case of the abelian $H$ the $G/H$ chiral gauged theory is
equivalent to a particular $(G\times H)/H$ gauged WZNW theory. In contrast to
the gauged WZNW model, the chiral gauged one admits a (1,0) supersymmetric
extension which is consistent at the quantum level. Integrating out the $2d$
gauge field we determine the exact (in $\alpha'$) form of the couplings of the
corresponding heterotic sigma model. While in the bosonic (superstring) cases
all the fields depend (do not depend) non-trivially on $\alpha'$ here the
metric receives only one $O(\alpha')$ correction while the antisymmetric tensor
and the dilaton remain semiclassical. As a simplest example, we discuss the
basic $D=3$ solution which is the heterotic string counterpart of the `black
string' $SL(2,R) \times R/ R $ background.
