Season the chicken breasts with salt and pepper on both sides.
In a large skillet, heat olive oil and butter over medium heat. Once hot, add the chicken breasts and sear until golden brown on both sides, about 5-7 minutes per side. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for about 3-4 minutes until soft.
Add the minced garlic to the mushrooms and sauté for an additional minute until fragrant.
Pour in the balsamic vinegar, scraping any browned bits from the bottom of the skillet. Let it simmer for about 1-2 minutes.
Lower the heat and stir in the heavy cream, mixing well until combined.
Return the chicken breasts to the skillet, coating them in the creamy mushroom sauce. Let simmer for another 5-7 minutes, or until the chicken is cooked through (internal temperature should reach 165°F).
Adjust seasoning with additional salt and pepper, if desired.
Garnish with fresh chopped parsley before serving.
Notes
Serve over mashed potatoes or pasta for a complete meal.