Step 1

Light a grill. In a medium bowl, combine 1/4 cup of hoisin sauce with the soy sauce, honey, grated ginger, minced garlic, chili-garlic sauce and sesame oil. Season the barbecue sauce with salt and pepper.

Step 2

Brush the chicken lightly with vegetable oil and season with salt and pepper. Grill the chicken over a hot fire, turning occasionally, until golden and almost cooked through, about 10 minutes. Brush with the barbecue sauce and grill, turning and brushing, until golden brown, about 3 minutes longer. Transfer the chicken to a work surface and let stand for 5 minutes, then cut it into 1/2-inch strips.

Step 3

Arrange the chicken and lettuce on a platter. Allow guests to make their own wraps by brushing a small amount of hoisin sauce on a lettuce leaf, topping it with cucumber, scallions, chicken and a squeeze of lime and rolling it up.