  We construct new topological theories related to sigma models whose target
space is a seven dimensional manifold of G_2 holonomy. We define a new type of
topological twist and identify the BRST operator and the physical states.
Unlike the more familiar six dimensional case, our topological model is defined
in terms of conformal blocks and not in terms of local operators of the
original theory. We also present evidence that one can extend this definition
to all genera and construct a seven-dimensional topological string theory. We
compute genus zero correlation functions and relate these to Hitchin's
functional for three-forms in seven dimensions. Along the way we develop the
analogue of special geometry for G_2 manifolds. When the seven dimensional
topological twist is applied to the product of a Calabi-Yau manifold and a
circle, the result is an interesting combination of the six dimensional A- and
B-models.
