Cut large stems from chard, and slice the stems; set aside. Stack chard leaves, and roll into cylinders. Cut cylinders crosswise to make 1-inch strips; set aside.
Heat butter and oil in a large Dutch oven. Add shallots and garlic; sauté for 3 minutes. Add chard stems, and sauté for 2 minutes. Gradually add chard leaves, and sauté for 5 minutes or until tender. Stir in salt and pepper.