  We consider the generalization of the heterotic action considered by Cherkis
and Schwarz where the chiral bosons are introduced in a manifestly covariant
way using an auxiliary field. In particular, we construct the kappa-symmetric
heterotic action in ten-dimensional supergravity background coupled to super
Yang-Mills theory and prove its kappa-symmetry. The usual Bianchi identity of
Type I supergravity with super Yang-Mills $dH_3= -\tr F\wedge F$ is crucially
used. For technical reason, the Yang-Mills field is restricted to be abelian.
