Preheat the oven to 375ºF. (See recipe notes for grilling instructions.) Grease a 9X13 baking dish and set aside.
Pound the chicken breasts evenly to about one inch thickness. This will allow them to cook evenly and decrease the baking time. Place the chicken in the prepared baking dish and liberally season with salt and pepper.
Divide the pesto on top of each breast and spread evenly. Scatter the tomatoes around the chicken.
Bake 25 -30 minutes, or until the internal temperature measures 165ºF.
Once the chicken is cooked through, remove from the oven, reposition the oven rack to the top position. Turn on the broiler. Top the chicken with the mozzarella and broil for 1-2 minutes, or until the cheese is melted and starts to brown. Garnish with fresh basil, if desired.
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Grilled Pesto Chicken:Spread the pesto on each side of the chicken breast after seasoning with salt and pepper. Preheat the grill to medium-high. Place the tomatoes on a large piece of heavy duty foil, folded up along the edges to prevent them from rolling off.
Cook the chicken on side side of the grill, about 5 minutes per side, while the tomatoes cook on the other side. Once the chicken has cooked through, move the chicken to foil with the tomatoes and sprinkle the cheese on top. Close the cover, grill for 1-2 minutes, or until the cheese melts.Stuffed Pesto Mozzarella Chicken:Slice the chicken breasts along one side, lengthwise, to create a pocket. Open the chicken, spread the pesto on the inside, and then stuff with the mozzarella.Close the chicken, season the tops with salt and pepper and spread on a little more pesto, if desired. The baking time will increase 5-10 minutes, but be sure to use an instant read thermometer to ensure it's cooked through before serving.