In a large stock pot, add rice, celery, green onion and chicken broth. Bring to a boil, then add chopped chicken. Turn heat to simmer, cover and cook for about 30 minutes, or until chicken is cook through and celery is tender.

Mean while, in a medium sauce pan, slowly melt butter. Gradually add in flour, while constantly stirring to allow flour to be free of lumps. Add salt and pepper, and continue stirring, until all flour has been added.

Slowly add milk to butter/flour mixture. Continue stirring to dissolve butter/flour mixture. Increase heat, if necessary. When all milk has been added and butter mixture is dissolved, remove from heat.

Slowly add milk solution to chicken broth and heat gently, but do not boil.