Add olive oil and ground chicken to a large non-stick skillet. Cook and crumble chicken over medium-high heat until browned. Drain any fat.
Stir in garlic, onion, hoisin sauce, soy sauce, rice wine vinegar, ginger, and Sriracha until onions have become translucent, about 1 to 2 minutes.
Stir in chestnuts and green onions until tender, about 1 to 2 minutes; season with salt and pepper, to taste.
Spoon several tablespoons of the chicken mixture into the center of a lettuce leaf. Top with shredded carrots, if desired. Serve immediately and enjoy!
