For a fresh pasta dish, toss bow-tie pasta with chicken, pesto, and red pepper strips.
Bring a pot of salted water to a boil. Season chicken with salt and pepper. Warm oil in a large skillet over medium-high heat. Cook chicken until no longer pink inside, 5 to 6 minutes per side. Let rest on a cutting board for 5 minutes, then cut into 1/2-inch pieces.
Add pasta to boiling salted water and cook until done, about 11 minutes or as package label directs. Drain well, return to pot and stir in pesto. Add chicken and red-pepper strips. Toss and season with salt and pepper. Sprinkle with grated Parmesan, if desired, and serve.