Heat olive oil in a nonstick pan. Add chicken and cook over medium heat 6 to 8 minutes, until lightly browned. Add garlic and thyme and cook 30 seconds more. Remove chicken from pan and keep warm.
Add broccoli to pan and saute for 30 seconds. Add 1/2 cup hot water and cover. Cook about 4 minutes, until broccoli is slightly soft. Bring a large pot of lightly salted water to a boil. Add pasta and cook according to package directions.
Add chicken to broccoli and remove pan from heat. When pasta is done, drain and add to pan. Stir and sprinkle with cheese.