Cut chicken meat in 1/4-inch strips.
Heat oil in a Dutch oven over medium-high heat. Add carrot and basil; saute 1 minute. Add celery, green onion and onion; saute 1 minute. Add salt, pepper, and chicken; saute 5 minutes. Add barley; saute 1 minute.
Add broth; bring to a boil. Cover, reduce heat, and simmer 40 minutes. Remove from heat. Stir in parsley and cheese.