  We study an algebraic deformation problem which captures the data of the
general deformation problem for a quantum vertex algebra. We derive a system of
coupled equations which is the counterpart of the Maurer-Cartan equation on the
usual Hochschild complex of an assocative algebra. We show that this system of
equations results from an action principle. This might be the starting point
for a perturbative treatment of the deformation problem of quantum vertex
algebras. Our action generalizes the action of the Kodaira-Spencer theory of
gravity and might therefore also be of relevance for applications in string
theory.
