Bring oil to high heat in a wok or large frying pan. Saute chicken breasts for 4 to 5 minutes per side or done. Remove chicken from the pan and cool. Keep oil in the pan, keep hot. As chicken cools mince water chestnuts and mushrooms to about the size of small peas. Prepare the stir fry sauce by mixing the soy sauce, brown sugar, and rice vinegar together in a small bowl. When chicken is cool, mince it as the mushrooms and water chestnuts are. With the pan still on high heat, add another Tbsp of vegetable oil. Add chicken, garlic, onions, water chestnuts and mushrooms to the pan. Add the stir fry sauce to the pan and saute the mixture for a couple minutes then serve it in the lettuce"cups".