  A hypercomplex manifold $M$ is a manifold equipped with three complex
structures satisfying quaternionic relations. Such a manifold admits a
canonical torsion-free connection preserving the quaternion action, called
Obata connection. A quaternionic Hermitian metric is a Riemannian metric on
which is invariant with respect to unitary quaternions. Such a metric is called
HKT if it is locally obtained as a Hessian of a function averaged with
quaternions. HKT metric is a natural analogue of a Kahler metric on a complex
manifold. We push this analogy further, proving a quaternionic analogue of
Buchdahl-Lamari's theorem for complex surfaces. Buchdahl and Lamari have shown
that a complex surface M admits a Kahler structure iff $b_1(M)$ is even. We
show that a hypercomplex manifold M with Obata holonomy $SL(2,{\mathbb H})$
admits an HKT structure iff $H^{0,1}(M)=H^1({\cal O}_M)$ is even.
