Season the chicken breasts with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken breasts and cook for about 5-7 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and garlic. Sauté for about 2-3 minutes until the onion is translucent and fragrant.
Add the sliced mushrooms to the skillet and cook for another 5 minutes, until they are soft and releasing their moisture.
Pour in the chicken broth and balsamic vinegar, scraping up any brown bits from the bottom of the skillet. Bring to a simmer and let it reduce for 3-5 minutes.
Stir in the heavy cream, dried thyme, and rosemary, allowing the sauce to thicken slightly.
Return the chicken to the skillet, coating it in the creamy mushroom sauce, and let it simmer for an additional 3-4 minutes to warm through.
Taste and adjust the seasoning with salt and pepper if needed.
Remove from heat and garnish with chopped fresh parsley before serving.
Notes
Serve with garlic mashed potatoes or steamed green beans for a colorful presentation.