  A hypercomplex manifold is by definition a smooth manifold equipped with two
anticommuting integrable almost complex structures. For example, every
hyperkaehler manifold is canonically hypercomplex (the converse is not true).
For every hypercomplex manifold M, the two almost complex structures define a
smooth action of the algebra of quaternions on the tangent bundle to M. This
allows to associate to every hypercomplex manifold M of dimension 4n a certain
almost complex manifold X of dimension 4n+2, called the twistor space of M.
When M is hyperkaehler, X is well-known to be integrable. We show that for an
arbitrary hypercomplex manifold its twistor space is also integrable.
