A search for charginos and neutralinos, predicted by supersymmetric theories, has been performed using a data sample of 2.6 pb(-1) at a centre-of-mass energy of root s = 130 GeV and 2.6 pb(-1) at 136 GeV collected with the OPAL detector at LEP during November 1995. No candidate events were observed. The 95% C.L. lower limit on the lightest chargino mass in the Minimal Supersymmetric Standard Model is 65.4 GeV if the universal scalar mass m(o) is greater than 1 TeV, and 58.7 GeV for the smallest m(o) compatible with slepton and sneutrino mass limits obtained at centre-of-mass energies near the Z peak. These limits were obtained under the conditions that the lightest chargino is heavier than the lightest neutralino by more than 10 GeV and tan beta is larger than 1.5. The results of a model independent search for charginos and neutralinos are also given.