In a small bowl, whisk the ingredients for the sauce. Set aside.
Heat one tablespoon of avocado oil in a large pan over medium/high heat. Add the broccoli and bell peppers to the pan. Cook for 2-3 minutes, stirring frequently.
Remove the veggies from the pan, and add the other tablespoon of avocado oil. Place the chicken pieces in the pan, making sure not to overcrowd the pan. Brown for 1-2 minutes on each side.
Once the chicken is done browning, pour the sauce into the pan. Once the sauce starts bubbling, reduce the heat to low. Simmer for 2-3 minutes. Then add the veggies back into the pan and simmer for 3-4 more minutes.