  A hypercomplex structure on a smooth manifold is a triple of integrable
almost complex structures satisfying quaternionic relations. The Obata
connection is the unique torsion-free connection that preserves each of the
complex structures. The holonomy group of the Obata connection is contained in
$GL(n, \mathbb{H})$. There is a well-known construction of hypercomplex
structures on Lie groups due to Joyce. In this paper we show that the holonomy
of the Obata connection on SU(3) coincides with $GL(2, \mathbb{H})$.
