  This work is the first step in a two-part investigation of real-time replica
wormholes. Here we study the associated real-time gravitational path integral
and construct the variational principle that will define its saddle-points. We
also describe the general structure of the resulting real-time replica wormhole
saddles, setting the stage for construction of explicit examples. These saddles
necessarily involve complex metrics, and thus are accessed by deforming the
original real contour of integration. However, the construction of these
saddles need not rely on analytic continuation, and our formulation can be used
even in the presence of non-analytic boundary-sources. Furthermore, at least
for replica- and CPT-symmetric saddles we show that the metrics may be taken to
be real in regions spacelike separated from a so-called `splitting surface'.
This feature is an important hallmark of unitarity in a field theory dual.
