  We construct a microlocalization of the rational Cherednik algebras $H$ of
type $S_n$. This is achieved by a quantization of the Hilbert scheme
$\Hilb^n\C^2$ of $n$ points in $\C^2$. We then prove the equivalence of the
category of $H$-modules and the one of modules over its microlocalization under
certain conditions on the parameter.
