In a large, deep skillet or wok, heat oil over medium to high heat.
Add sliced chicken, broccoli, and peppers. Sauté, stirring frequently until the chicken is cooked through and the broccoli is crisp-tender. Add the garlic and cook for one minute.
While the chicken and vegetables are pan-frying, add all the sauce ingredients to a bowl or measuring cup. Stir to completely combine.
When the chicken and veggies are done, give the sauce mixture one more quick stir and pour into skillet. Stir to coat mixture with sauce. Cook 1 to 2 minutes, stirring occasionally, until sauce is thickened.
Serve over with rice and sprinkle with chopped green onions.