Deligne's conjecture on the operadic action on Hochschild cochains

Let $\mathcal{A}$ be an associative algebra, let $\mathcal{C}^\bullet(\mathcal{A},\mathcal{A})$ be its Hochschild complex, and let $C_2$ be the little-disks operad in dimension two. Write $\mathsf{Chains}(C_2)$ for the operad of chains on $C_2$.

Deligne's conjecture. There exists a natural action of the operad $\mathsf{Chains}(C_2)$ on the Hochschild complex $\mathcal{C}^\bullet(\mathcal{A},\mathcal{A})$ for any associative algebra $\mathcal{A}$.

This conjecture asserts that Hochschild cochains carry a natural structure governed by the chains on the little-disks operad. The supplied text does not state whether the conjecture has been proved or remains open.