Fillet the chicken breasts into two thinner pieces (or pound the chicken to an even thickness then cut each breast in half to create four portions). Season the chicken with a pinch of salt and pepper on both sides.

Heat a large skillet over medium heat. Once hot, add 1 tablespoon oil and swirl to coat the surface. Add the chicken to the skillet and cook on each side until golden brown and cooked through (about 7-10 minutes total). Remove the chicken to a clean plate.

Turn the heat down to medium-low. Add the remaining olive oil to the skillet along with the minced garlic and halved grape tomatoes. Sauté for about five minutes, or until the tomatoes start to soften and lose their shape.

Add the heavy cream and pesto to the skillet with the tomatoes and stir to combine. Allow the sauce to come up to a simmer. Taste the sauce and adjust the salt or pepper to your liking.

Add the chicken back to the skillet with the tomatoes and sauce, turning to coat the chicken. Allow the chicken to simmer in the sauce for just a few minutes more to heat through. Serve hot.