  We propose a notion of algebra of {\it twisted} chiral differential operators
over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such
algebras possess families of modules depending on infinitely many complex
parameters, which we classify in terms of the corresponding algebra of twisted
differential operators. If the underlying manifold is a flag manifold, our
construction recovers modules over an affine Lie algebra parameterized by opers
over the Langlands dual Lie algebra. The spaces of global sections of
"smallest" such modules are irreducible $\ghat$-modules and all irreducible
$\frak{g}$-integrable $\ghat$-modules at the critical level arise in this way.
