To make the marinade: place all the ingredients (except the chicken) in a blender and blend on high until smooth. Place the chicken in a large zip-top bag and pour the marinade on top. Seal the bag and place in the refrigerator for at least 2 hours, up to 8, turning the bag occasionally.
Combine the ingredients for the dipping sauce and set aside.
Preheat a grill over medium-high heat. Once the grill is hot, remove the chicken from the marinade, shaking any excess off. Grill 4-5 minutes per side until lightly charred and the internal temperature reaches 165 degrees F. Remove the chicken from the grill and rest for 5 minutes.
Serve grilled chicken with steamed rice, lettuce cups, fresh herbs, limes, and sliced cucumbers and shallots.