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Combine all marinade ingredients in a bowl. Reserve 1/3 cup (85 ml) of marinade in another bowl to use as dipping sauce. Pour marinade into a resealable plastic bag and add chicken. Rub chicken in bag to work in marinade. Let marinate in the fridge for at least 2 hours.
Add 3 tbsp. (45 ml) water to reserved marinade and mix well. Set aside.
Preheat BBQ on high and grill chicken on a well-oiled grill, using indirect heat by turning off burner directly under chicken and leaving opposite burner on high. Grill 6 minutes per side. When chicken is cooked, cut it into strips.
On a large serving plate, arrange all toppings, chicken, and sauce. Take a leaf of lettuce, garnish it with rice, the toppings of your choice, and chicken. Gently close the lettuce leaf to form a wrap, dip in the sauce, and enjoy.