In 3-quart saucepan, heat oil over medium heat. Cook chicken, onion, chili powder and salt in oil, stirring frequently, until chicken is browned. Stir in broth. Heat to boiling; reduce heat to medium. Simmer uncovered 5 minutes.
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Meanwhile, in medium bowl, mix Bisquick mix and milk until soft dough forms. Fold in cilantro, cumin and chile. Drop dough by 10 spoonfuls onto simmering soup. Cook uncovered 10 minutes. Cover; cook 10 minutes longer.