Cut the chicken breasts in half lengthwise, and beat the thicker part of the chicken until it is even in thickness. Season the chicken with salt and pepper on both sides.
Heat the oil in a large skillet over medium/high heat. Once hot, add the chicken and cook on each side until golden brown and cooked through, 4-5 minutes per side.
Remove the chicken to a plate and cover to keep warm.
Turn the heat down to medium/low. To the same skillet, add the butter, garlic and tomatoes. Sauté for about two minutes.
Add the heavy cream, broth, and pesto to the skillet and stir to combine: cook until the sauce starts to thicken.
Return the chicken to the skillet with the tomatoes and sauce, turning to coat the chicken. Cook until the chicken is reheated.
Serve and enjoy, friends.