Sauté first 4 ingredients in 3 tablespoons hot oil in a Dutch oven 5 minutes. Add chopped chicken and next 6 ingredients. Bring mixture to a boil; reduce heat, and simmer 30 minutes. Discard bay leaf.
Fry tortilla strips in 1/2 cup hot oil in a large skillet until crisp. Drain on paper towels.
Sprinkle fried strips and cheese over each serving. Top with avocado, if desired.
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