Add stew meat to a large casserole and cover with water. Bring to a boil and remove any film or residue from the surface. Turn down to a simmer and cook for ten minutes. Add onion, tomato, celery, meat seasoning, and basic green chile and continue cooking over low heat, just above a simmer. When meat begins to become fork tender (about 1 hour) add carrots and continue cooking for 15 minutes. Just before serving, add potatoes, adjust seasoning, and serve when potatoes are cooked through.