Melt 1 Tbl. butter in heavy small skillet over medium heat. Add shallots and garlic; sauté until transparent, about 1 minute. Transfer shallot mixture to bowl.
Add remaining 7 Tbl. butter, 1 Tbl. Worcestershire sauce, 1 tsp. dry mustard and 2 Tbl. chives and stir with fork to blend. Season to taste with salt and pepper.
Place plastic wrap on work surface. Transfer butter mixture to plastic wrap and form butter into 5-inch-long log. Roll up in plastic, enclosing completely.
Refrigerate until firm.