In a small saucepan, bring 2 cups water to a boil. Add the tea bags and star anise and steep for 5 minutes, then discard the tea bags and star anise. Stir in the soy sauce, brown sugar, vegetable and sesame oils and cinnamon; let cool to room temperature, about 10 minutes.
Place the chicken breasts in a gallon-size resealable plastic bag and pour in the marinade; refrigerate for at least 1 hour or up to 8 hours.
Preheat a grill to medium. Position the chicken on an oiled cooking grate and then grill, uncovered and turning onto each side twice, until cooked through, 10 to 12 minutes.