Inspect the crab meat for any remaining shell fragments and discard them.

In a large mixing bowl, whisk together the mayonnaise, lemon juice, Dijon mustard, Old Bay seasoning, salt, and pepper until smooth.

Add the finely diced celery and chopped chives to the dressing mixture.

Gently fold in the crab meat using a rubber spatula, taking care not to break up the large lumps.

Cover and refrigerate for at least 30 minutes to allow flavors to meld before serving.

Serve chilled on a bed of lettuce, in a brioche bun, or with crackers.