  We prove the $\Gamma$-convergence of the renormalised Gaussian fractional
$s$-perimeter to the Gaussian perimeter as $s\to 1^-$. Our definition of
fractional perimeter comes from that of the fractional powers of
Ornstein-Uhlenbeck operator given via Bochner subordination formula. As a
typical feature of the Gaussian setting, the constant appearing in front of the
$\Gamma$-limit does not depend on the dimension.
