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Yes, the holonomy of this manifold is in $SU(n)$. Indeed, the Chern connection on the canonical bundle is flat and its holonomy preserves $\Omega$, because its curvature is $\partial\bar\partial |\Omega|^2=0$. However, the Chern connection on canonical bundle is indused by the Levi-Civita connection on $M$, hence the Levi-Civita connection also satisfies $\nabla\Omega=0$.