Add olive oil to a large saucepan over medium-high heat. Add ground chicken breast and cook through, about 5 minutes. Drain any excess fat.
Add the minced garlic, onion, chili garlic sauce, hoisin sauce, soy sauce, rice wine vinegar. Stir together and cook for 1 minute. Stir in water chestnuts, and continue to cook about 1-2 minutes; season with salt and pepper, to taste.
Serve by spooning several big tablespoons onto butter lettuce leaves. Top with green onions and additional chili garlic sauce, if desired.