  The Kodama State is unique in being an exact solution to all the ordinary
constraints of canonical quantum gravity that also has a well defined
semi-classical interpretation as a quantum version of a classical spacetime,
namely (anti)de Sitter space. However, the state is riddled with difficulties
which can be tracked down to the complexification of the phase space necessary
in its construction. This suggests a generalization of the state to real values
of the Immirzi parameter. In this first part of a two paper series we show that
one can generalize the state to real variables and the result is surprising in
that it appears to open up an infinite class of physical states. We show that
these states closely parallel the ordinary momentum eigenstates of
non-relativistic quantum mechanics with the Levi-Civita curvature playing the
role of the momentum. With this identification, the states inherit many of the
familiar properties of the momentum eigenstates including delta-function
normalizability. In the companion paper we will discuss the physical
interpretation, CPT properties, and an interesting connection between the inner
product and the Macdowell-Mansouri formulation of general relativity.
