We obtain new five-dimensional supersymmetric rotating multi-Kaluza-Klein black hole solutions with the Godel parameter in the Einstein-Maxwell system with a Chern-Simons term. These solutions have no closed timelike curve outside the black hole horizons. At the infinity, the space-time is effectively four-dimensional. Each horizon admits various lens space topologies L(n;1)=S^3/Z_n in addition to a round S^3. The space-time can have outer ergoregions disjointed from the black hole horizons, as well as inner ergoregions attached to each horizon. We discuss the rich structures of ergoregions.
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