Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Drain and set aside.
In a large skillet or sauté pan, heat olive oil over medium-high heat. Season chicken with fajita seasoning, salt, and pepper. Cook the chicken until browned and cooked through, about 5–7 minutes. Remove and set aside.
In the same pan, add sliced bell peppers and onion. Sauté for 4–5 minutes until tender. Add garlic and cook for an additional 30 seconds.
Pour in chicken broth and bring to a simmer. Stir in heavy cream and shredded cheese. Cook, stirring constantly, until the cheese melts and the sauce becomes smooth and creamy.
Return the cooked chicken and pasta to the pan. Toss everything together until the pasta is fully coated in sauce and everything is evenly mixed. Heat for another 2–3 minutes until warmed through.
Serve hot, garnished with fresh cilantro and lime wedges if desired.