Heat olive oil in a large skillet over medium heat.
Season the chicken breasts with salt and pepper, then add them to the skillet.
Remove the chicken from the skillet and set aside.
In the same skillet, add diced onion and sliced mushrooms, sauté until softened.
Stir in minced garlic and thyme, cooking for an additional 1-2 minutes.
Deglaze the skillet with Riesling, scraping up any browned bits from the bottom.
Stir in heavy cream and return the chicken to the skillet, simmering gently.
Continue to cook for an additional 10-15 minutes, or until the chicken is cooked through.
Adjust seasoning with salt and pepper as needed before serving.