Heat oil in a large skillet over medium-high. Add onion and cook until soft, about 3 minutes. Stir in garlic and ginger, cooking for 1 minute.
Add ground chicken, breaking it up with a spoon. Cook until no longer pink, about 5 minutes.
Stir in hoisin, soy sauce, rice vinegar, and sriracha. Cook for 2 minutes, letting everything mingle.
Toss in water chestnuts and green onions. Cook for another 2 minutes, then season with salt and pepper.
Spoon the mixture into lettuce cups, sprinkle with sesame seeds, and dig in!