A search for R-parity conserving charginos and neutralinos, predicted by supersymmetric theories, is performed using a data sample of about 435pb^-1 taken at centre-of-mass energies of 192 to 209GeV with the OPAL detector at LEP in the years 1999 and 2000. No evidence for chargino or neutralino production is found. Upper limits on chargino and neutralino pair production (chi+_1 chi-_1, chi^0_1 chi^0_2) cross-sections are obtained as a function of the chargino mass, the lightest neutralino mass and the second lightest neutralino mass.