Heat olive oil in a large saute pan over medium heat. Add the chicken and cook for about 5 minutes, breaking it into small pieces as it cooks, until browned.
Add the garlic, ginger, onion, carrot, teriyaki sauce, orange sauce, tamari, maple syrup and rice wine vinegar. Toss the mixture to coat all of the chicken. Cook until onions become translucent, about 5 minutes.
Stir in the water chestnuts and the green onions and cook 1-2 minutes.
Serve in a bowl, with another plate or bowl of lettuce leaves. Each person can scoop the chicken mixture onto the lettuce leaves and eat like a taco.