1In shallow glass or plastic dish, mix 1/4 cup of the dressing and the chives. Add chicken; turn to coat. Cover; refrigerate 1 to 2 hours, turning chicken occasionally.
2Heat gas or charcoal grill. Place chicken on grill over medium heat. Cover grill; cook 15 to 20 minutes, turning once or twice, until juice of chicken is clear when center of thickest part is cut (170°F). Add bacon to grill for last 2 to 3 minutes of cooking time to heat. If desired, add buns, cut sides down, for last 4 minutes of grilling or until toasted.
3In small bowl, mix remaining 1/4 cup dressing, the mayonnaise and parsley; spread on cut sides of buns. Layer bacon, chicken, tomato and cucumber in each bun.