Coat a nonstick pan with cooking spray; sauté chicken over medium-high heat until cooked through. Remove from pan. Add oil and sauté garlic and ginger until garlic is golden. Add vegetables; cook until tender. Return chicken to pan; stir-fry 3 minutes.
For the sauce, whisk 1 1/2 tbsp hot (not boiling) tap water into peanut butter to blend. Add soy sauce, vinegar, and hot sauce and mix. Divide stir-fry and sauce onto 2 plates. Serve each over 3/4 cup brown rice.
