Using 2.0fb-1 of integrated luminosity collected by the CDFII experiment at the Tevatron ppbar collider at root(s)=1.96TeV, we present a search for supersymmetry using the three lepton and missing energy signature of chargino-neutralino production. We expect to see about 12 supersymmetric events for a suitable choice of parameters in the mSUGRA model. Our observation of seven events is consistent with the Standard Model expectation of 6.4+-1.1 events. We rule out chargino masses below 141GeV/c2 in certain mSUGRA regions and also present results in a model-independendent fashion.