Heat oil in a large nonstick skillet over medium-high heat. Add the onion, garlic, thyme, and mushrooms; sauté 5 minutes or until onion is tender. Add chicken; sauté 4 minutes or until the chicken is lightly browned. Add wine, salt, and pepper; cook 3 minutes or until liquid almost evaporates.
Stir in rice and broth. Bring to a boil; cover, reduce heat, and simmer 5 minutes or until liquid is absorbed. Stir in cheese and parsley.