1. Combine first 9 ingredients in a large zip-top plastic bag. Add chicken to bag; seal and marinate in refrigerator at least 6 hours or up to 24 hours, turning bag occasionally.
2. Remove chicken from bag, reserving marinade. Pour marinade into a large skillet; stir in broth. Arrange chicken in a bamboo steamer coated with cooking spray; cover with steamer lid.
3. Place bamboo steamer in pan; bring marinade mixture to a boil. Steam the chicken 18 minutes or until a thermometer inserted in center of breasts registers 165°. Transfer chicken to a platter.
4. Remove steamer from pan. Strain marinade mixture through a fine sieve into a bowl; discard solids. Return marinade mixture to pan; bring to a boil over high heat. Cook until reduced to 1/2 cup (about 2 minutes). Serve sauce with chicken.
Wine note: This recipe includes lots of savory elements, like soy and hoisin sauce, making it suitable for lighter red wines. Li Veli Passamante 2005 ($12) is made from Italy's negroamaro grapes and offers layers of dried cherries, blueberry, and herbs. The wine's light body and bright acid, along with its soft tannins, allow it to match this dish's complexity without overpowering it. —Jeffery Lindenmuth