Heat oil over medium-low heat in a saucepan. Add garlic, onion, bell pepper and Italian seasoning.
Cook until onions and pepper are soft, about 5 minutes, stirring frequently. Add the diced tomatoes and remaining seasonings. Cover the pan and simmer over low heat for 15 minutes, stirring occasionally. Add the chicken, stir, cover and simmer for an additional 15 minutes. Add the vinegar to the pan and stir. Set aside.
Steam the kohlrabi noodles according to the instructions on the bag.
Spoon the tomato sauce over the noodles, garnish with fresh basil, and serve immediately.