Combine the rice and water in a saucepan over medium-high heat. Bring to a boil, then reduce heat to low, cover, and simmer for 20 minutes, or until rice is tender. In a small bowl, stir together the soy sauce, peanut butter, vinegar, and cayenne pepper. Set aside.
Heat oil in a skillet or wok over high heat. Add chicken, garlic and ginger, and cook, stirring constantly, until chicken is golden on the outside, about 5 minutes.
Reduce heat to medium, and add green onion, broccoli, peanuts, and the peanut butter mixture. Cook, stirring frequently, for 5 minutes, or until broccoli is tender, and chicken is cooked through. Serve over rice.