In a large skillet, place the chicken breasts and cover them with water. Bring to a boil, then reduce the heat and simmer for about 20 minutes, or until the chicken is cooked through.
Remove the chicken from heat, let cool, and then shred or dice the chicken into bite-sized pieces.
In a large mixing bowl, combine the shredded chicken, chopped celery, halved grape tomatoes, and finely chopped red onion.
In a separate small bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, salt, and pepper until well combined.
Pour the dressing over the chicken and vegetable mixture. Gently fold the ingredients together until everything is well coated with the dressing.
If desired, add chopped fresh parsley for an extra burst of flavor and color.
Taste and adjust seasoning as necessary, adding more salt, pepper, or lemon juice according to your preference.
Serve immediately or chill in the refrigerator for 30 minutes for a colder salad.