Pound chicken as needed to even out the thickness of the breasts. Pat dry with paper towels, then season with salt and pepper.
Heat the oil in a nonstick skillet over medium heat. Add the chicken to the skillet and coo until lightly brown on both sides, about 4 minutes. Remove chicken from the skillet to a plate and set aside..
Add the onion and 1/4 teaspoon salt to the skillet and cook over medium heat until softened, about 5 minutes.
Stir in the remaining ingredients while scraping up any browned bits for the bottom of the skillet.
Turn the heat to low. Place the chicken to the skillet, with any accumulated chicken juice, and coat with the sauce.
Cover and simmer until the chicken is fully cooked through, about 10 minutes. Serves 4 people.