In a small bowl, whisk the hoisin sauce, rice wine vinegar, soy sauce, and sesame oil until well blended
In a large skillet, over med-high heat, heat olive oil. Add onions and cook until soft, about 5 minutes. Stir in ginger and garlic and cook for about 1 minute. Add ground chicken and cook until just done, about 5 minutes. Break up the meat as it cooks.
Pour in the sauce and cook for an additional 2 minutes, until the sauce reduces slightly and the chicken has finished cooking completely.
Remove from heat and add in water chestnuts and green onions.
Season to taste with salt and pepper
Build wraps by placing lettuce leaf on a plate. Add a scoop of white rice in the center, then top with the chicken mixture. Repeat with remaining lettuce leaves.