Heat olive oil over medium heat in large soup pot or Dutch oven. Cook onions, celery, carrots and garlic until soft, about 8 minutes. Add thyme, salt and pepper, stir, and cook another minute to let vegetables absorb seasonings.
Add water and chicken stock to pot and bring to a boil. Add barley and reduce heat. Cover and simmer for 45 minutes, or until barley is thoroughly cooked.
Stir in diced chicken and fresh green beans. Cover and simmer an additional 15 minutes.
Immediately stir in Parmesan cheese until dissolved. Serve.