In 5- to 6-quart saucepan or Dutch oven, heat oil over medium heat. Add chicken; cover and cook 4 to 6 minutes, stirring occasionally, until no longer pink in center.
Stir in remaining ingredients except cilantro. Heat to boiling. Reduce heat to medium-low; cover and simmer about 20 minutes, stirring occasionally, until zucchini is tender.
Stir in cilantro; cook 3 minutes longer, stirring occasionally.