We construct new heterotic string backgrounds which are analogous to s
uperstring solutions corresponding to coset models but are not simply
the ''embeddings'' of the latter. They are described by the (1,0) supe
rsymmetric extension of the G/H chiral gauged WZNW models. The ''chira
l gauged'' WZNW action differs from the standard gauged WZNW action by
the absence of the AABAR-term (and thus is not gauge invariant in the
usual sense) but can still be expressed as a combination of WZNW acti
ons and is conformally 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 x H)/H gauged WZNW theory. In contrast to the gauged WZNW model, th
e chiral gauged one admits a (1,0) supersymmetric extension which is c
onsistent at the quantum level. Integrating out the 2d gauge field we
determine the exact (in alpha') form of the couplings of the correspon
ding heterotic sigma model. While in the bosonic (superstring) cases a
ll the fields depend (do not depend) nontrivially on alpha' here the m
etric receives only one O(alpha') correction while the antisymmetric t
ensor and the dilaton remain semiclassical. As a simplest example, we
discuss the basic D = 3 solution which is the heterotic string counter
part of the ''black string'' SL(2, R) x R/R background.