In the Dutch oven place the oil, chicken base, diced onion, garlic, cumin, chili, and cayenne. Saute until the onions are soft and clear, about 5 minutes.
In a bowl, combine Masa Harina with 1-quart water. Stir until all lumps dissolve and it looks like a paste.Tip: The Masa Harina must be mixed into the 1 quart of water completely. If the masa harina is added directly into the soup it is difficult to mix and will become lumpy.
Add the masa harina to the Dutch oven with the sauteed onions then bring almost to a boil. Once the mixture starts to bubble, continue to simmer for 2-3 minutes, stirring constantly.Tip: This step eliminates any raw taste from Masa Harina.
Slowly add to the Dutch oven the remaining 3 quarts of water while stirring to incorporate the paste and water.
Add the crushed tomatoes then let the soup return to a gentle boil while stirring occasionally.
Add the diced cheese to the soup while continuing to simmer and stirring occasionally, until the cheese melts.
Add chicken then simmer to heat through. Leave on a gentle simmer until ready to serve.