To begin, cut the chicken into 1 inch chunks and place it in a bowl. Toss it with a tablespoon of the balsamic vinegar. Set it aside.
In a bowl, combine the remaining vinegar, soy sauce, ketchup, cornstarch, sugar, and water. Whisk those together until smooth. Set aside.
Heat a tablespoon of cooking oil in a non-stick skillet. Toss in the chicken. Cook over medium heat until opaque.
Meanwhile, dice the onion and mince the garlic. When the chicken is opaque, scoop it out into a dish and set it aside.
Wipe the skillet out with a paper towel. Add in another tablespoon or so of oil and toss in your onions. Allow those to cook until slightly tender and then toss in the garlic and carrots. Cook and stir about 2 minutes.
Return the chicken to the skillet and pour in your sauce.
Toss in the water chestnuts and pineapple chunks. Stir it together and cook it covered for about 4-5 more minutes or until the chicken is just done.