Place chicken breasts in the bowl of a food processor and process until the chicken is finely chopped, being careful to not over-process into a paste.
Place chicken into a mixing bowl and set aside.
Cut celery stalk into 1 to 2 inch pieces and place in food processor bowl.
Process celery until it is very finely chopped.
Place celery into bowl with chicken.
Add mustard and mix well. If you are not sure how you will like a spread heavy on Dijon, start with half and taste after adding half of the mayonnaise.
Add half of mayonnaise and mix well. Taste now if you used half of the Dijon. Add the remaining Dijon for a stronger flavor, more mayonnaise for a lighter flavor.
More Dijon and/or mayonnaise can be added to adjust the consistency, use whichever one or a combination of both to suit your tastes.
Add salt and pepper to taste.
Place in a covered container and refrigerate until chilled.