In a large pot, place the oil, chicken base, onion, cumin, chili powder, garlic powder and cayenne pepper. Saute until the onions are soft and translucent, about 5 minutes.
In a bowl, combine the masa harina and 4 cups water. Stir until all lumps are dissolved. Add to the onion mixture and bring to a boil. Once the mixture starts to bubble, continue cooking 2-3 minutes, stirring constantly. This will eliminate any raw taste from the masa harina.
Add remaining 4 cups water and the tomatoes. Return to a boil, stirring occasionally. Add American cheese gradually, waiting until thoroughly melted before adding more, stirring constantly until all cheese is melted. Add chicken and cook until heated through.
Ladle into bowls and garnish with crumbled tortilla chips, salsa and shredded cheddar cheese.