In a pot, bring water to a boil and add the chicken breasts. Cook for about 15-20 minutes, or until the chicken is fully cooked. Remove from heat and allow to cool, then chop into bite-sized pieces.
In a mixing bowl, combine the chopped chicken, diced celery, halved grapes, and finely chopped red onion.
In a separate smaller bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, salt, and pepper. Adjust seasoning to taste.
Pour the dressing over the chicken mixture and stir gently to combine, ensuring everything is evenly coated.
Serve the chicken salad on a bed of mixed greens if desired, or enjoy it on its own.
For extra flavor, consider adding chopped apples, nuts, or fresh herbs such as dill or parsley to the salad before serving.