The derived Maurer-Cartan locus

The derived Maurer-Cartan locus $\text{MC}^\bullet(L)$ is a functor from differential graded Lie algebras to cosimplicial schemes. If L is differential graded Lie algebra, let $L_+$ be the truncation of $L$ in positive degrees $i>0$. We prove that the differential graded algebra of functions on the cosimplicial scheme $\text{MC}^\bullet(L)$ is quasi-isomorphic to the Chevalley-Eilenberg complex of $L_+$.