  The bulk partition function of pure Chern-Simons theory on a three-manifold
is a state in the space of conformal blocks of the dual boundary RCFT, and
therefore transforms non-trivially under the boundary modular group. In
contrast the bulk partition function of AdS(3) string theory is the
modular-invariant partition function of the dual CFT on the boundary. This is a
puzzle because AdS(3) string theory formally reduces to pure Chern-Simons
theory at long distances. We study this puzzle in the context of massive
Chern-Simons theory. We show that the puzzle is resolved in this context by the
appearance of a chiral "spectator boson" in the boundary CFT which restores
modular invariance. It couples to the conformal metric but not to the gauge
field on the boundary. Consequently, we find a generalization of the standard
Chern-Simons/RCFT correspondence involving "nonholomorphic conformal blocks"
and nonrational boundary CFTs. These generalizations appear in the
long-distance limit of AdS(3) string theory, where the role of the spectator
boson is played by other degrees of freedom in the theory.
