  A module M over a vertex algebra V is half-integrable if a_n act locally
nilpotently on M for all a in V, m in M, n>0. We study half-integrable modules
over sheaves of twisted chiral differential operators (TCDO) on a smooth
variety X. We prove an equivalence between certain categories of
half-integrable modules over TCDO and categories of (twisted) D-modules on X.
