Heat oil in a large nonstick skillet. Add pork and cook over medium-high heat until it's no longer pink. Transfer to plate.
Stir-fry onion and garlic for 1 minute. Add peppers; stir-fry until onions are tender. In a cup, mix broth, soy sauce and cornstarch. Add to vegetables and stir-fry until thickened, 2 to 3 minutes. Stir in oyster sauce and water chestnuts and cook until heated through, 1 to 2 minutes.