Cook the rice according to the package directions.
Meanwhile, heat the oil in a wok or large saucepan over medium-high heat.
Add the cabbage and carrots and cook, stirring occasionally, until just tender, 3 to 5 minutes.
Add the water chestnuts, chicken, and soy sauce and cook until heated through, 2 to 3 minutes.
Divide the rice among plates, spoon the vegetables over top, and sprinkle with the peanuts. Serve with the teriyaki sauce, if desired.