Bring a large pot of lightly salted water to a boil. Add linguine pasta, and cook for 8 to 10 minutes, or until al dente; drain.
Meanwhile, place chicken and Cajun seasoning in a bowl, and toss to coat.
In a large skillet over medium heat, saute chicken in butter until no longer pink and juices run clear, usually about 5 to 7 minutes. Remove the chicken, leaving the skillet on high heat. Add the olive oil and, when heated, add the garlic, peppers and onions and cook for 1 to 2 minutes. Add the tomatoes and cook for another 30 seconds. Remove all the vegetables from the skillet.
With the skillet still over high heat, pour in the chicken broth and wine. Cook for 3 to 5 minutes, scraping the bottom of the pan as needed. Reduce heat to medium-low and pour in the cream, stirring constantly. Cook the sauce over medium-low heat for a few minutes, until the cream starts to thicken the mixture. Taste and add freshly ground black pepper, cayenne pepper, and salt to taste.
Add the chicken and vegetables to the sauce, making sure to include all the juices that have drained onto the plate. Stir and cook until the mixture is bubbly and hot, 1 to 2 minutes. Add the drained fettuccine and toss to combine.
Top with chopped fresh parsley or parmesan cheese.
