The formality conjecture for the chiral deformation algebra of $SK$

Let $K$ be a finitely generated free ${\cal D}_X$-module, and let $SK$ denote the associated chiral algebra. Let $\mathrm{def}_{SK}$ be its deformation pro-$*$-Lie algebra, and let $H_{SK}$ be the corresponding cohomology pro-$*$-Lie algebra. Two perfect pro-$*$-Lie algebras are perfectly quasi-isomorphic when they are connected by a chain of perfect quasi-isomorphisms. Formality conjecture. $\mathrm{def}_{SK}$ and $H_{SK}$ are perfectly quasi-isomorphic. This is the chiral analogue of Kontsevich's formality theorem. The supplied text gives no resolution of the conjecture.