Slice each chicken breast into two thinner pieces, or pound them to even thickness and cut each breast horizontally to make four portions. Season both sides with a pinch of salt and pepper.
Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the chicken and cook until golden brown and fully cooked, about 7–10 minutes total, flipping once. Transfer the chicken to a clean plate.
Lower the heat to medium-low. Add the remaining olive oil to the skillet, then the minced garlic and halved grape tomatoes. Cook for about 5 minutes, stirring occasionally, until the tomatoes soften and start to break down.
Pour in the heavy cream and pesto, stirring to combine with the tomatoes. Let the sauce come to a gentle simmer. Taste and adjust with more salt or pepper if needed.
Return the chicken to the skillet, turning to coat it in the creamy pesto sauce. Simmer for a few more minutes until the chicken is heated through. Serve hot and enjoy!