Prolate-oblate shape coexistence close to the ground state in the strongly-deformed proton-rich A approximate to 120nuclei is reported for the first time. One of the four reported bands in Cs-119, built on a 11/2- state at 670 keV, consists of nearly degenerate signature partners, and has properties which unequivocally indicate the strongly-coupled pi h(11/2)[505]11/2(-) configuration associated with oblate shape. Together with the decoupled pi h(11/2[)541]3/2(-) band built on the 11/2- prolate state at 110 keV, for which a half-life of T-1/2 = 55(5) mu shas been measured, the new bands bring evidence of shape coexistence at low spin in the proton-rich strongly deformed A approximate to 120 nuclei, a phenomenon predicted since long time, but not yet observed. Calculations using the particle-number conserving cranked shell model and two dimensional tilted axis cranking covariant density functional theory support and well reproduce the observed oblate and prolate coexisting low-energy states in Cs-119.