Bring 4 cups water to a boil in a 3-qt. heavy saucepan; add tea bags. Remove from heat; cover and steep 10 minutes.
Discard tea bags. Stir in sugar and next 6 ingredients, stirring until sugar dissolves. Cool completely (about 45 minutes); stir in ice. (Mixture should be cold before adding chicken.).
Place tea mixture and chicken in a large zip-top plastic freezer bag; seal. Place bag in a shallow baking dish and chill 24 hours. Remove chicken from marinade, discarding marinade; pat chicken dry with paper towels.
Light one side of grill, heating to 300° to 350° (medium) heat; leave other side unlit. Place chicken, skin side down, over unlit side, and grill, covered with grill lid, 20 minutes. Turn chicken, and grill, covered with grill lid, 40 to 50 minutes or until done. Transfer chicken, skin side down, to lit side of grill, and grill 2 to 3 minutes or until skin is crispy. Let stand 5 minutes before serving.