Add the mayonnaise, Dijon mustard, lemon juice, Old Bay seasoning, Worcestershire sauce, salt, and black pepper to a small mixing bowl.
Whisk until the sauce is smooth, creamy, and evenly combined. Scrape down the sides of the bowl as needed to remove any streaks of mustard or seasoning.
Fold in the finely chopped chives until they are evenly distributed throughout the sauce.
Cover the bowl and refrigerate for at least 15 minutes before serving. This gives the flavors time to blend and helps the sauce taste more balanced.
Serve chilled with crab cakes as a dipping sauce, or spoon a small amount over each crab cake just before serving.