Preheat your oven to 450 degrees F. Grease a rimmed baking dish or line it with parchment paper.
Place the chicken breasts in the prepared baking dish. Spray them with oil and sprinkle them with salt and pepper. Bake for 20 minutes.
Carefully remove the baking dish from the oven. Spread 2 tablespoons of pesto sauce on the top of each chicken breast. Arrange 2 tomato slices on top, and sprinkle them with 2 tablespoons of shredded mozzarella.
Return the chicken to the oven. Bake until cooked through and the cheese is melted, about 5 more minutes. If your baking dish is broiler-safe, you can finish by broiling for 1-2 minutes to brown the cheese.
The best way to ensure that the chicken is cooked through is to use an instant-read thermometer inserted into the thickest part. Aim for an internal temperature of 165 ºF.You can make this recipe with boneless skinless chicken thighs. They'll cook faster than chicken breasts, so at the first stage of cooking, try just 15 minutes instead of 20 minutes. But after the dish is done, do use a thermometer to make sure the chicken is fully cooked.