Bose-Einstein condensation has been achieved in a magnetically trapped sample of 85Rb atoms. Long-lived condensates of up to 10^4 atoms have been produced by using a magnetic-field-induced Feshbach resonance to reverse the sign of the scattering length. This system provides many unique opportunities for the study of condensate physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a very wide range. This range extended from very strong repulsive to large attractive self-interactions. When the interactions were switched from repulsive to attractive, the condensate shrank to below our resolution limit, and after ~5 ms emitted a burst of high-energy atoms.