Season the chicken generously with salt and freshly ground black pepper. Heat oil in a wok over medium-high heat. Sear chicken until beautifully browned, approximately 5 minutes. Remove chicken and set aside on a plate.
Saute bell peppers and onion in the hot wok for 5 minutes. Add mixed vegetables, bean sprouts, and water chestnuts; saute for an additional 2 minutes. Return chicken to the wok, pour in soy sauce and teriyaki, and cook until chicken is fully cooked, about 5 minutes.