In a large skillet over medium-high, heat the olive oil. Add the onion, mushrooms and garlic, then saute for 4 minutes.
Add the chicken and cook, turning to brown evenly, for 4 minutes. Stir the onions and mushrooms as needed to prevent burning.
Add the chicken broth and thyme, bring to a simmer, then reduce heat to simmer. Partially cover and cook for 12 to 15 minutes, or until the chicken reads 165 F at the thickest part. Check the liquid level now and again and add additional broth as needed.
Transfer the chicken to a plate and cover with foil to keep warm. Return the skillet to medium heat. Remove the thyme stems.
In a small glass, mix together the starch and water. Add to the skillet and cook, stirring constantly, until thickened. Remove the pan from the heat and whisk in the sour cream. Season with salt and pepper.