  This is the first of two papers in which we prove that a cell model of the
moduli space of curves with marked points and tangent vectors at the marked
points acts on the Hochschild co--chains of a Frobenius algebra. We also prove
that a there is dg--PROP action of a version of Sullivan Chord diagrams which
acts on the normalized Hochschild co-chains of a Frobenius algebra. These
actions lift to operadic correlation functions on the co--cycles. In
particular, the PROP action gives an action on the homology of a loop space of
a compact simply--connected manifold.
  In this first part, we set up the topological operads/PROPs and their cell
models. The main theorems of this part are that there is a cell model operad
for the moduli space of genus $g$ curves with $n$ punctures and a tangent
vector at each of these punctures and that there exists a CW complex whose
chains are isomorphic to a certain type of Sullivan Chord diagrams and that
they form a PROP. Furthermore there exist weak versions of these structures on
the topological level which all lie inside an all encompassing cyclic
(rational) operad.
