Boil the penne in salted water according to package instructions. Drain and set aside.
In a large skillet, heat olive oil over medium-high heat. Season the chicken with salt and pepper. Add the chicken strips to the pan and sauté until browned and cooked through, about 5–7 minutes. Remove and set aside.
In the same skillet, add a little more oil if needed. Add the sliced bell peppers and cook until just tender, about 4–5 minutes. Stir in garlic and chipotle peppers and cook for 1 more minute until fragrant.
Reduce heat to medium. Stir in the honey and lime juice, then pour in the heavy cream. Simmer for 2–3 minutes, then stir in the parmesan cheese. Let cook until the sauce thickens slightly, about 3–4 minutes.
Add the cooked pasta and chicken back into the skillet. Toss everything together until evenly coated with the sauce and heated through.
Serve immediately, garnished with chopped parsley or cilantro and optional red pepper flakes for a kick.