Heat vegetable oil in a large skillet over medium-high heat.
Add ground chicken and cook for 5-7 minutes, breaking it up with a wooden spoon into small crumbles, until browned and cooked through.
Add garlic and ginger to the pan and cook for 1 minute until fragrant.
Stir in water chestnuts, soy sauce, hoisin sauce, rice vinegar, sesame oil, and sriracha, cooking for 2-3 minutes until heated through.
Remove from heat and stir in sliced green onions.
Spoon the chicken mixture into individual lettuce leaves and serve immediately, allowing everyone to assemble their own wraps.