We prove that a given Calabi-Yau threefold with a stable holomorphic vector
bundle can be perturbed to a solution of the Strominger system provided that
the second Chern class of the vector bundle is equal to the second Chern class
of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy
then the equations of motion derived from the heterotic string effective action
are also satisfied by the solutions we obtain.Comment: 19 pages, late
