1. To prepare cocktail sauce, combine chili sauce, juice, dill, and horseradish in a small bowl.
2. To prepare chive butter, combine butter and chives in a small bowl; cover and keep warm.
3. To prepare shellfish, place wine and Old Bay in a large Dutch oven; set a large vegetable steamer in pan. Bring wine mixture to a boil over high heat.
4. Add clams to steamer. Steam clams, covered, for 8 minutes. Add mussels to steamer. Steam mussels and clams, covered, for 8 minutes or until clam and mussel shells open. Discard any unopened shells, and discard wine mixture. Serve shellfish immediately with sauces.