Rinse chicken; pat dry. Heat oil in a 12-inch skillet; add chicken. Cook chicken, uncovered, over medium heat for 10 minutes. Turn chicken; add onion and cook 5 minutes more or until chicken and onion are lightly browned. Drain off fat. Carefully add 1-1/4 cups of the beer, the brown sugar, red pepper, and salt.
Bring to boiling; reduce heat. Simmer, covered, for 15 minutes. Uncover; add bananas and cook for 12 minutes more or until chicken is cooked through.
Using a slotted spoon, remove chicken, onion, and banana to a platter; cover to keep warm. Measure remaining liquid and, if necessary, add water to total 1 cup.
Return chicken and liquid mixture to skillet. Combine remaining 1/4 cup beer and cornstarch; add to skillet. cook and stir over medium heat until thickened and bubbly; cook for 1 to 2 minutes more. Serve chicken and sauce over hot rice, if desired. Makes 6 servings.