For no-cook wraps, chop up roasted chicken from the grocery store or deli. For a low carb lettuce wrap with ground chicken, heat olive oil in a saucepan over medium high heat. Add ground chicken and cook until browned, about 3-5 minutes, making sure to crumble the chicken as it cooks; drain excess fat.
Mix together the garlic, onion, hoisin sauce, soy sauce, rice wine vinegar, ginger and Sriracha. Saute in olive oil until onions have become translucent, about 1-2 minutes (if using ground chicken, saute in the same pan as chicken). Season with salt and pepper, to taste.
To serve, spoon several tablespoons of the chicken mixture into the center of a lettuce leaf, taco-style and enjoy.