Bring a large pot of salted water to a boil and cook the pasta according to package instructions until al dente; reserve 1/2 cup pasta cooking water, then drain the pasta.
Toss the chicken pieces with the fajita seasoning until evenly coated.
Heat the olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook 2–3 minutes per side, or until browned and cooked through; remove any large pieces if needed so they cook evenly.
Add the sliced bell pepper, sliced onion, and minced garlic to the skillet and sauté 2–3 minutes, stirring, until the onion is tender and the peppers begin to soften.
Pour in the heavy cream and the reserved 1/2 cup pasta water, bring to a gentle simmer, then return the drained pasta to the skillet.
Stir in the shredded cheddar cheese and simmer, stirring occasionally, about 5 minutes until the cheese melts and the sauce thickens and coats the pasta and chicken.
Adjust seasoning to taste, then serve immediately.
