Season the chicken with half the salt and black pepper.
Heat the oil in a 12-inch skillet over medium-high heat. Add the chicken and cook for 5 minutes, stirring occasionally. Add the mushrooms and cook for 3 minutes or until tender, stirring occasionally. Add the garlic and cook and stir for 30 seconds. Season with the remaining salt and black pepper.
Reduce the heat to medium-low. Stir in the sauce. Cover and cook for 5 minutes or until the mixture is hot and bubbling. Remove the skillet from the heat. Stir in the peas. Add the penne and toss to coat.