  A quaternionic version of the Calabi problem was recently formulated by M.
Verbitsky and the author. It conjectures a solvability of a quaternionic
Monge-Ampere equation on a compact HKT manifold (HKT stays for HyperKaehler
with Torsion). In this paper this problem is solved under an extra assumption
that the manifold admits a flat hyperKaehler metric compactible with the
underlying hypercomplex structure. The proof uses the continuity method and a
priori estimates.
