Cook the chicken breasts until fully cooked and tender. You can bake, boil, or poach them. Once cooked, allow the chicken to cool slightly, then dice into bite-sized pieces.

In a large mixing bowl, combine the mayonnaise, sour cream, Dijon mustard, lemon juice, and sweet pickle relish. Stir well to create a smooth dressing.

Add the finely chopped celery, red onion, and fresh dill (if using) to the dressing. Mix well to evenly distribute the ingredients.

Add the diced chicken to the bowl with the dressing. Gently fold the chicken into the mixture until all pieces are evenly coated with the dressing.

Season the chicken salad with salt and pepper to taste. Adjust the amount of mayonnaise, sour cream, or mustard if necessary to achieve your desired consistency and flavor.

Cover the chicken salad and refrigerate for at least 30 minutes to allow the flavors to meld. Serve chilled on a bed of lettuce, as a sandwich filling, or with crackers.