Heat 1 tablespoon olive oil in large pan over medium-high heat. Add onions and peppers and cook until tender, 3 to 4 minutes. Remove from heat and let cool slightly.
With a sharp paring knife, slice into the chicken horizontally to create a pocket. Repeat with all four breasts. Add a slice of cheese into each chicken breast and stuff with 1/4 cup of the pepper mix. Top peppers with another slice of cheese. Press the edges of the chicken together to seal in the filling. Rub all sides of chicken breast with 1/2 tablespoon Cajun seasoning and a pinch of salt and pepper.
Heat the remaining olive oil in the same pan over medium heat. Cook the stuffed chicken for 5-7 on each side, until cheese is melted and chicken is cooked through.