In a small bowl, whisk together the mayonnaise, diced celery, diced celery leaves, dried dill, white pepper and salt. Cover and refrigerate the dressing for 30 minutes to allow the flavors to meld. (This dressing can also be prepared the day before and refrigerated overnight.)
Slice each red grape in half lengthwise.
Assemble the sandwiches:
Split a biscuit in half, and spread a teaspoon of the dressing on each half of the biscuit. Tear a lettuce leaf in half and place a half on the bottom half of the biscuit. Top the lettuce with 1 ounce of the chicken breast slices (fold/twist the chicken slices to fit them to the biscuit and to give them a nice presentation.)
Place 4 or 5 grape halves on top of the chicken and then finish with the top half of the biscuit. Stick a sandwich pick or toothpick down through the top of the sandwich to hold everything together. Place the sandwich on a serving tray. Repeat these steps with the remaining biscuits and fillings.
Serve the sandwiches immediately. The tray of sandwiches can also be covered with plastic wrap and refrigerated for up to 2 hours before serving.