Cook pasta according to package directions for al dente. Reserve 1 cup of pasta water, and then drain. Set aside.
Slice chicken into strips. Heat the olive oil in a large skillet over medium heat. Cook the chicken strips, sliced bell peppers and sliced onions until soft and chicken is cooked through, about 12-15 minutes. Remove from pan onto a separate plate.
Melt the butter in the same pan and add minced garlic. Saute the garlic until it turns golden brown.
Stir in the cream, tomato paste, Parmesan cheese, fajita seasoning and salt. Simmer until thickened. Use reserved pasta water to thin the sauce, if desired.
Add the pasta, chicken, onions and peppers back in and toss to coat.