We report the result of a search for charginos and neutralinos, in e+e− collisions at 189 GeV centre-of-mass energy at LEP. No evidence for such particles is found in a data sample of 176 pb−1. Improved upper limits for these particles are set on the production cross sections. New exclusion contours in the parameter space of the Minimal Supersymmetric Standard Model are derived, as well as new lower limits on the masses of these supersymmetric particles. Under the assumptions of common gaugino and scalar masses at the GUT scale, we set an absolute lower limit on the mass of the lightest neutralino of 32.5 GeV, and a limit on the mass of the lightest chargino of 67.7 GeV for M2<2 TeV.