  We study conformal field theories for strings propagating on compact,
seven-dimensional manifolds with G_2 holonomy. In particular, we describe the
construction of rational examples of such models. We argue that analogues of
Gepner models are to be constructed based not on N=1 minimal models, but on Z_2
orbifolds of N=2 models. In Z_2 orbifolds of Gepner models times a circle, it
turns out that unless all levels are even, there are no new Ramond ground
states from twisted sectors. In examples such as the quintic Calabi-Yau, this
reflects the fact that the classical geometric orbifold singularity can not be
resolved without violating G_2 holonomy. We also comment on supersymmetric
boundary states in such theories, which correspond to D-branes wrapping
supersymmetric cycles in the geometry.
