In a large skillet, heat 1 tablespoon of olive oil at medium high heat. Add onion and bell pepper and cook while stirring for 5 minutes. Add spinach, 1 teaspoon of rosemary, 1/2 teaspoon of salt and 1/4 teaspoon black pepper and cook while stirring for 3 minutes or until spinach had softened. Remove skillet from the heat and let cool slightly. Add cheese and stir. Set aside. In a small bowl, mix remaining of oil, rosemary salt and pepper.
With a sharp knife, cut each chicken breast horizontaly on the thickest side, in a way to do a pocket. Stuff each pocket of 3 to 4 tablespoons of the spinach mixture. Fix each pocket with a tooth-pick. With the fingers, brush each side of the chicken breasts with the mixture of rosemary.
Set the bbq to medium high heat. Put the stuffed chicken breasts on oiled grill. Close the cover of the bbq and cook 10 to 12 minutes on each side or until chicken is not pink inside.