Bring first 3 ingredients to boil in heavy medium saucepan. Reduce heat, add chicken and simmer until almost cooked through, turning occasionally, about 12 minutes. Transfer chicken to plate; cool. Remove chicken skin and bones. Cut meat into 1/2-inch pieces.
Strain soup through sieve into small saucepan. Add 1 tablespoon lime juice and jalapeño to soup and simmer until reduced to 2 cups, about 20 minutes. Add chicken and simmer just to heat through. Taste, adding more lime juice if desired. Ladle soup into bowls. Sprinkle with fresh cilantro.
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