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 broccoli and the peanut butter mixture. Cook, stirring frequently, for 10 minutes, or until broccoli is tender, and chicken is cooked through. If the sauce is getting too thick, thin with chicken broth as needed.
Put into a serving bowl and top with chopped peanuts.