Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. When the oil is hot, add in the onion, peppers, and plenty of salt and pepper. Sauté the vegetables until they are very tender and then transfer them to a plate.
Add the remaining tablespoon of olive oil to the skillet. Lay sliced chicken in a single layer in skillet. Sprinkle with seasonings. Let chicken cook without moving it for a couple minutes so that it browns.
When the chicken is fully cooked, add the onions, peppers, and any juices left on the plate. Stir everything together. Top it with the shredded provolone cheese. Cover skillet until cheese melts. Serve immediately.