Cook the pasta in well salted water according to the "al dente" instructions on the box. This will keep the pasta firm to allow for absorption of the vinegar. Be sure to retain 1/4 cup of the pasta water.

Heat the olive oil in a large skillet over medium-high heat. When it begins to shimmer, add the chicken and season with salt and pepper. The chicken should be cooked through in about 8 minutes.

Meanwhile, steam or boil the broccoli for 3 minutes. Add the broccoli to the chicken after the chicken is cooked.

Add the garlic to the skillet and stir. Let it cook for about 1 minute.

Put the pasta in the skillet with the 1/4 cup of pasta water to deglaze the pan. Add the balsamic vinegar and stir to mix everything thoroughly and to get it all coated with the balsamic vinegar, about 1-2 minutes.

Serve with parmesan cheese and garnish with fresh parsley if desired.