Rinse chicken and pat dry; cut into 1-inch chunks. In a bowl, combine chili powder, cumin, and turmeric. Add chicken and mix to coat.
Pour oil into a 12-inch frying pan or 14-inch wok over high heat; when hot, add onion, garlic, and ginger. Stir until onion is limp, about 2 minutes. Add chicken and stir until white on the outside but still slightly pink in the middle (cut to test), about 3 minutes.
Meanwhile, in a 2-cup glass measure, mix chicken broth, vinegar, bean paste, soy sauce, and sugar. Add to pan along with zucchini and green beans. Bring to a boil and cook, stirring occasionally, until vegetables are barely tender to bite and chicken is no longer pink in the center (cut to test), about 5 minutes. Pour into a serving dish.