  Let $\mathcal{A}_{crit}$ be the chiral algebra corresponding to the affine
Kac-Moody algebra at the critical level $\hat{\mathfrak{g}}_{crit}$. Let
$\mathfrak{Z}_{crit}$ be the center of $\mathcal{A}_{crit}$. The commutative
chiral algebra $\mathfrak{Z}_{crit}$ admits a canonical deformation into a
non-commutative chiral algebra $\mathcl{W}_{h}$. In this paper we will express
the resulting first order deformation via the chiral algebra
$\mathcal{D}_{crit}$ of chiral differential operators of $G((t))$ at the
critical level.
