Heat the olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and black pepper. Add the chicken to the skillet and cook for about 6-7 minutes on each side, or until cooked through and golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, reduce the heat to medium and add the minced garlic. Sauté for about 1 minute until fragrant, being careful not to burn it.
Pour in the heavy cream and pesto sauce, stirring to combine. Bring the mixture to a gentle simmer and let it cook for 2-3 minutes, allowing it to thicken slightly.
Stir in the grated Parmesan cheese until melted and smooth. Return the cooked chicken to the skillet, coating it with the creamy sauce. Cook for an additional 2-3 minutes to heat through.
Serve the creamy garlic pesto chicken hot, garnished with fresh parsley. Enjoy with pasta, rice, or a side salad.