Cook penne according to the package directions. Once cooked, measure out ½ cup of the pasta water and set aside for later. Drain the pasta and set aside.
Meanwhile, in a large skillet, heat 2 tablespoons of olive oil over medium heat. Add chicken to pan and cook for approximately 5 to 8 minutes, stirring occasionally. You want to cook the chicken until juices run clear and chicken is no longer pink. Sprinkle salt and pepper on the chicken and mix well.
Add red, yellow, orange peppers and shallots to pan. Cook for 4 to 7 minutes, allowing peppers and shallots to brown on edges. Add garlic and cook for 1 minute longer.
Add balsamic vinegar, lemon juice, 1 tablespoon olive oil and ½ cup reserved pasta water and cooked penne pasta to pan. Cook for about 3 to 4 minutes, stirring while ingredients come together.