Excited states have been observed for the first time in the very neutron-deficient 55114Cs59 nucleus. The assignment to Cs114 was made by detecting γ rays in coincidence with evaporated charged particles and with recoiling evaporation residues. A rotational band has been observed up to spin 21 (tentatively 25). Excitation-energy systematics and a study of quasiparticle alignments suggest that the band is based on the ν(h11/2)π(h11/2) configuration. Unlike bands based on this configuration in heavier cesium isotopes, only one signature partner is observed, and there is no evidence for signature inversion. These observations agree with theoretical calculations which predict that Coriolis-induced signature splitting should dominate at N=59.