This invention provides a method of inhibiting viable cells transplanted into a subject from being destroyed by the subject's immune system which comprises: a) containing the viable cells, or tissue comprising the viable cells, prior to transplantation within a device comprising a semipermeable membrane; and b) treating the subject with a substance which inhibits an immune-system costimulation event in an amount effective to inhibit the subject's immune system from responding to said contained cells or tissue. In one embodiment, the substance which inhibits an immune-system costimulation event is CTLA4. Also provided by this invention is a method of treating diabetes in a subject which comprises: a) containing viable insulin-producing cells, or tissue comprising such cells, within a device comprising a semipermeable membrane; b) transplanting an effective amount of such contained viable insulin-producing cells into the subject; and c) treating the subject with an effective amount of a substance which inhibits an immune-system costimulation event.