String topology is the study of the free loop space of a manifold
LM.  The loop product, defined on the homology of LM, is described
intuitively as a combination of the intersection product on M and
loop concatenation in the based loop space of M.  However, since the
intersection product is well-defined only on transversally intersecting
chains, this description is incomplete. Brown's theory of twisting
cochains provides a chain model of a bundle in terms of the chains on
the base and chains on the fiber.  We extend this theory so that it can
be applied to provide a model of the free loop space. We give a precise
definition of the loop product defined at the chain level.