Cut the chicken into 1-inch cubes. Toss with the teriyaki sauce and let sit for 10 minutes.
Heat the oil in a large skillet over high heat until it starts to shimmer. Add the broccoli and red pepper strips and cook for 2 minutes, stirring. Add the water chestnuts and cook for 1 minute, stirring. Remove the vegetables from the pan and reserve.
Add the chicken and teriyaki sauce to the pan. Cook, stirring for about 4 minutes or until the chicken is cooked through. Add the vegetables back to the pan and cook for 1 minute more.