Place the chicken strips and balsamic vinegar in a large resealable plastic bag.
Seal the bag securely and turn it several times to coat the chicken evenly.
Refrigerate the chicken for at least 15 minutes.
Heat the olive oil in a large skillet over medium heat.
Add the sliced onion and sliced garlic to the skillet.
Sauté for 1 minute, stirring frequently.
Remove the chicken from the refrigerator.
Drain and discard the balsamic vinegar marinade.
Add the chicken strips to the skillet with the onion and garlic.
Cook for 4 to 5 minutes, stirring occasionally, until the chicken is cooked through and the juices run clear.
Stir in the crushed tomatoes, roasted red peppers, red pepper flakes, chicken broth, Italian seasoning, and salt.
Bring the mixture to a boil over medium heat.
Cook and stir for 4 to 5 minutes, or until the sauce is heated through.
Reduce the heat to low.
Simmer the chicken and sauce mixture for 15 minutes, stirring occasionally.
While the sauce is simmering, cook the penne pasta according to the package directions.
Drain the cooked pasta thoroughly.
Add the drained penne pasta to the chicken and roasted pepper sauce.
Toss until the pasta is evenly coated with the sauce and the chicken mixture is well distributed.
Sprinkle the shredded Parmesan cheese over the pasta.
Serve warm.