If accessible at LEP II, chargino production is likely to be one of the few available supersymmetric signals for many years. We consider the prospects for the determination of fundamental supersymmetry parameters in such a scenario. The study is complicated by the dependence of observables on a large number of these parameters. We propose a straightforward procedure for disentangling these dependences and demonstrate its effectiveness by presenting a number of case studies at representative points in parameter space. Working in the context of the minimal supersymmetric standard model, we find that chargino production by itself is a fairly sensitive probe of the supersymmetry-breaking sector. For significant regions of parameter space, it is possible to test the gaugino mass unification hypothesis and to measure the gaugino contents of the charginos and neutralinos, thereby testing the predictions of grand unification and the viability of the lightest supersymmetric particle as a dark matter candidate. For much of the parameter space, it is also possible to set limits on the mass of the electron sneutrino, which provide a valuable guide for future particle searches.