In a medium saucepan, cook onion and garlic in hot oil over medium heat until onion is tender. Stir in apple juice, tomato paste, vinegar, brown sugar, molasses, paprika, horseradish, Worcestershire sauce, salt, and pepper. Bring to boiling; reduce heat. Simmer, uncovered, about 30 minutes or until sauce is desired consistency, stirring occasionally.
Brush on chicken during the last 10 minutes of grilling. Makes about 10 (2 tablespoon servings).