In a wide frying pan, heat oil over medium low heat until it shimmers. Reduce heat to low and add tomatoes, garlic, chilies, onions and cumin. Cook, uncovered, stirring occasionally, until the mixture is thick, about 30 minutes. Set aside to cool slightly.
Preheat oven to 400. Butter a 9 x 13 glass pan. In a large bowl, combine chicken, cheddar, sour cream and salt. Stir in tomato mixture. Pour into the pan.
Working quickly with the Phyllo, lay one sheet at a time over the chicken tomato mixture and brush thinly but thoroughly with melted butter. Continue until you're almost out of butter, then lay the last piece of phyllo and brush with butter. With a sharp knife, cut down thru layers of phyllo to make nine evenly spaced rectangular servings.
Bake 20 to 30 minutes or until filling is hot and phyllo is golden brown. Serve immediately.