Heat oil in 10-inch skillet over medium heat. Add livers; sprinkle with salt and pepper. Cook and stir livers in hot oil until brown, about 3 minutes; drain.

Heat wine to boiling in 1 1/2-quart saucepan; reduce heat. Simmer uncovered 1 minute. Stir in gravy and chicken livers. Heat to boiling; reduce heat. Simmer uncovered 5 minutes. Stir in butter until melted. Stir water into cornstarch. Stir cornstarch mixture gradually into sauce. Heat to boiling. Boil and stir 1 minute. Serve over rice.