Place chicken and water in a stockpot, and add onion, celery, and garlic. Cover, and bring to a boil. Reduce heat, and simmer until chicken is tender, about 45 minutes.
Remove chicken from broth, and set aside to cool. Skim off fat. Smash cooked garlic cloves against side of pot. Add undrained tomatoes, cumin, cayenne pepper, white pepper, and bouillon cube to the broth. Cover, and simmer 30 minutes.
Add corn, green onion, and cilantro. Simmer 10 minutes longer.
Skin and bone chicken, then dice or shred into bite-size pieces. Add chicken to soup along with cooked rice. Heat through. Season with salt to taste. Ladle into bowls, and garnish with cheese and tortilla chips.