  In this paper we introduce a notion of parallel transport for principal
bundles with connections over differentiable stacks. We show that principal
bundles with connections over stacks can be recovered from their parallel
transport thereby extending the results of Barrett, Caetano and Picken, and
Schreiber and Waldof from manifolds to stacks.
  In the process of proving our main result we simplify Schreiber and Waldorf's
definition of a transport functor for principal bundles with connections over
manifolds and provide a more direct proof of the correspondence between
principal bundles with connections and transport functors.
