In a very large pot over medium-high heat add in 2 tablespoons of oil and cook the beef stew meat until browned, which takes about 4-6 minutes. Remove and set aside.
Add the remaining 1 tablespoon of oil to the pot and cook the chicken until browned and cooked through, which takes about 4-6 minutes. Remove and set aside.
Add the onions to the pot and brown over medium-low heat while stirring every 1-2 minutes, which takes about 10 minutes.
Add the cooked beef and chicken back into the pot along with the beef stock and cook for 30 minutes over medium heat to help tenderize the meats.
Place in the carrots, celery, green beans, potatoes, corn, lima beans, and tomatoes and cook for 20-25 minutes over medium-low heat or until tender.
Finish with parsley, salt, and pepper and serve.