Heat oil in a large nonstick skillet over medium-high heat. Add chicken; sauté 5 minutes on each side. Remove from pan.
Add mushrooms, onion, and garlic to pan; sauté 5 minutes. Return chicken to pan. Add wine, broth, thyme, salt, and bay leaves; bring to a boil. Cover, reduce heat, and simmer 30 minutes. Discard bay leaves.
Combine milk and flour, stirring with a whisk. Stir milk mixture into pan; bring to a boil. Reduce heat; simmer 3 minutes or until thick, stirring often. Stir in pasta.