Place chicken breasts in a sauce pan and fill with water. Bring the pot to a boil, reduce to a simmer and cover the pot. Simmer for 14 minutes, remove the chicken breasts from the pot and allow to cool.
While the chicken breasts cool, whisk together mayonnaise, balsamic vinegar dried basil and black pepper in a large mixing bowl
Shred chicken breasts with 2 forks and place shredded chicken in the mixing bowl along with quartered cherry tomatoes, mozzarella cheese and fresh basil.
Toss to coat all of the ingredients in the mayo mixture evenly and serve.
Notes
You can use mini mozzarella pearls in place of cut mozzarella
You can use boneless skinless chicken thighs in place of chicken breast
If you don't like mayo, you can use plain greek yogurt in place of the mayonnaise