A search has been made for the chargino, the supersymmetric partner of theW ± (or the partner of the charged Higgs bosons), ine + e − annihilation at PETRA using the JADE detector. The chargino decay modes investigated are lv˜,lvˉγ˜,q1qˉ2γ˜ and q1qˉ2g˜ (with subsequent gluino decay g˜→qqˉγ˜ ). No evidence for such events has been observed. The 95% C.L. lower limit for the chargino mass is typically 22.5 GeV, depending only slightly on the masses of other supersymmetric particles. If the chargino is stable, the lower mass limit is 21.1 GeV (95% C.L.).