Season chicken breasts with dried rosemary, dried oregano, dried thyme, salt and pepper. Dredge the chicken in flour, shaking off any excess.
In a large skillet, heat the olive oil over medium-high heat and cook the chicken breasts for about 4-5 minutes on each side, or until golden brown and cooked through. Remove and set it aside.
In the same pan, add olive oil and the sliced mushrooms. Cook until they begin to release their moisture and turn golden brown, about 5 minutes.
Stir in the finely chopped onion and cook for about 2-3 minutes, or until the onion becomes translucent.
Add the garlic and sauté for 1 minute or until the garlic becomes fragrant.
Pour in the white vinegar and sugar (optional). Stir well and let it cook for a couple of minutes to reduce and thicken slightly.
Add the chicken stock and heavy cream to the pan. Simmer for about 10-15 minutes, or until the liquid reduces by about half.
Return the cooked chicken breasts to the pan and let them simmer in the sauce for another 5 minutes, allowing them to absorb the flavors and heat though.
Taste the sauce and adjust the seasoning if needed, and serve.