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

General Non-extremal Rotating Charged Godel Black Holes in Minimal Five-Dimensional Gauged Supergravity