In a large skillet, heat olive oil. Add chicken and brown on both sides, about 3-4 minutes each. Cover skillet and cook for 10 minutes more. (If chicken is not fully cooked all the way, that's okay. It will have a chance to finish cooking later.) Remove chicken from skillet and set aside.
Add diced green peppers, pineapple, crushed red pepper and ginger. Cook about 5 minutes. While cooking, cut the chicken into chunks.
Add reserved pineapple juice, teriyaki sauce and chicken stock. Bring to a boil, return chicken to skillet, reduce heat, cover and simmer for at least an additional 15 minutes or up to a few hours.
About 10 minutes before serving, remove cover from skillet and bring sauce back to a boil. Stir in cornstarch/water mixture and continue boiling until sauce is desired thickness.