  We present the general exact solutions for non-extremal rotating charged
black holes in the Godel universe of five-dimensional minimal supergravity
theory. They are uniquely characterized by four non-trivial parameters, namely
the mass $m$, the charge $q$, the Kerr equal rotation parameter $a$, and the
Godel parameter $j$. We calculate the conserved energy, angular momenta and
charge for the solutions and show that they completely satisfy the first law of
black hole thermodynamics. We also study the symmetry and separability of the
Hamilton-Jacobi and the massive Klein-Gordon equations in these
Einstein-Maxwell-Chern-Simons-Godel black hole backgrounds.
