A search was performed for charginos with masses close to the mass of the lightest neutralino in e+e− collisions at centre-of-mass energies of 189-209 GeV recorded by the OPAL detector at LEP. Events were selected if they had an observed high-energy photon from initial state radiation, reducing the dominant background from two-photon scattering to a negligible level. No significant excess over Standard Model expectations has been observed in the analysed data set corresponding to an integrated luminosity of 570 pb-1. Upper limits were derived on the chargino pair-production cross-section, and lower limits on the chargino mass were derived in the context of the Minimal Supersymmetric Extension of the Standard Model for the gravity- and anomaly-mediated Supersymmetry breaking scenarios.