  The Kodama State for Lorentzian gravity presupposes a particular value for
the Immirzi-parameter, namely $\beta=-i$. However, the derivation of black hole
entropy in Loop Quantum Gravity suggests that the Immirzi parameter is a fixed
value whose magnitude is on the order of unity but larger than one. Since the
Kodama state has de-Sitter spacetime as its classical limit, to get the proper
radiation temperature, the Kodama state should be extended to incorporate a
more physical value for $\beta$. Thus, we present an extension of the Kodama
state for arbitrary values of the Immirzi parameter, $\beta$, that reduces to
the ordinary Chern-Simons state for the particular value $\beta=-i$. The state
for real values of $\beta$ is free of several of the outstanding problems that
cast doubts on the original Kodama state as a ground state for quantum general
relativity. We show that for real values of $\beta$, the state is invariant
under large gauge transformations, it is CPT invariant (but not CP invariant),
and it is expected to be delta-function normalizable with respect to the
kinematical inner product. To aid in the construction, we first present a
general method for solving the Hamiltonian constraint for imaginary values of
$\beta$ that allows one to use the simpler self-dual and anti-self-dual forms
of the constraint as an intermediate step.
