If you haven't done so already, cook the chicken breasts by boiling or baking until fully cooked. Allow to cool, then shred or dice into bite-sized pieces.

In a large mixing bowl, combine the shredded chicken, mayonnaise, Dijon mustard, diced celery, halved grapes, and sliced almonds. This mixture will create a creamy and crunchy texture.

Add salt, black pepper, lemon juice, and fresh dill (if using) to the bowl. These ingredients enhance the flavor profile of the salad.

Using a wooden spoon or spatula, gently fold all the ingredients together until well combined. Be careful not to overmix, as you want to maintain the texture of the chicken and other ingredients.

Taste the chicken salad and adjust seasoning if necessary, adding more salt or pepper to your preference.

Serve immediately on a bed of lettuce, in a sandwich, or with crackers. For best flavor, refrigerate for 30 minutes before serving to allow the flavors to meld.