Mix flour, salt, pepper, and thyme in a shallow baking dish. Add chicken pieces one or two at a time to the flour mixture.
Add olive oil and butter to a large skillet over medium heat. Once butter has melted, begin adding floured chicken to the skillet and cook until browned on one side and turn over to brown lightly on the other side, about 3-5 minutes per side. Remove chicken pieces from the skillet with long tongs and place onto a plate. Continue the process until all chicken has been cooked.
Add mushrooms and garlic to the skillet and cook until the mushrooms become slightly browned and begin to become tender. Add marsala, scraping any browned bits from the bottom of the skillet. Stir in chicken stock and add back cooked chicken. Reduce heat and allow to simmer for about 12-15 minutes.