Sprinkle cornstarch, salt, and pepper over chopped chicken.
Heat 1 tablespoon oil in a large skillet. Add chicken and cook just until the outside browns; it doesn't need to be cooked all the way through. Remove from heat and set aside.
Add remaining oil to same skillet. Chop onion and peppers, and crush garlic; add all to hot skillet and cook for 3-4 minutes.
Add vinegar, water, soy sauce, and chicken, and cook until chicken is no longer pink. Remove from heat and stir in fresh basil.