Preheat grill. Soak wooden skewers or kitchen twine in shallow dish.

Cut a pocket in thickest side of each chicken breast and set aside. Melt butter in a medium skillet over medium heat. Add onion and garlic; saute until tender, about 5 minutes.

Add marjoram, parsley, thyme, salt, and bread crumbs to skillet; mix well. Spoon stuffing into chicken pockets; secure with wooden skewers or twine.

Combine melted butter and lemon peel in a small bowl. Grill chicken, basting frequently with butter mixture, about 12 minutes per side.