In a large skillet, brown chicken in oil; drain. Add broth. Bring to a boil. Reduce heat; cover and cook for 10 minutes.
Add the mushrooms, peas, red pepper, bamboo shoots and onions. Cover and cook 5-10 minutes longer or until a thermometer reads 180° and vegetables are tender.
Meanwhile, drain pineapple, reserving juice; set pineapple aside. In a small bowl, combine the cornstarch, reserved juice, vinegar, soy sauce and sugar. Pour into the skillet. Bring to a boil; cook and stir for 2 minutes or until thickened.
Stir in pineapple; heat through. Serve with noodles.