  Let $k$ be an algebraically closed field. Chambert-Loir proved that the
\'etale fundamental group of a normal rationally chain connected variety over
$k$ is finite. We prove that the fundamental group scheme of a normal
rationally chain connected variety over $k$ is finite and \'etale. In
particular, the fundamental group scheme of a Fano variety is finite and
\'etale.

Algebraic Geometry