In large pot, place oil, chicken base, onion and spices. Saute until onions are soft and clear, about 5 minutes. In another container, combine Masa Harina with 1 quart water. Stir until all lumps dissolve. Add to sauteed onions and bring to boil. Once mixture starts to bubble, continue cooking 2-3 minutes, stirring constantly. This will eliminate any raw taste from Masa Harina. Add remaining 3 quarts water to pot. Add tomatoes; let mixture return to boil stirring occasionally.
Add cheese to soup. Cook stirring occasionally, until cheese melts. Add chicken; heat through.