Heat vegetable oil in a large skillet over medium-high heat. Add chicken pieces to the skillet and cook until lightly browned and nearly cooked through, about 5 to 7 minutes.
Add broccoli florets to the skillet, pour the sauce over the chicken and broccoli, and stir to combine. Cover and let simmer for about 5 minutes, or until the broccoli is tender and the chicken is fully cooked.