In a medium sized skillet, heat oil over medium high heat in a large skillet. Cook the chicken on each side for about 7-10 minutes. Add the peppers and continue to cook until they become tender and chicken reads 165 degrees with a thermometer. Remove the chicken and veggies and set aside on a plate.
Add the soy sauce, water, peanut butter, white vinegar, brown sugar, garlic and lime juice. Whisk until it comes to a boil and reduce heat. Add chicken and veggies back to the skillet and let simmer for another 3-5 minutes.
Serve with steamed snow peas, red pepper flakes, and green onions over rice if desired.