Pound the chicken breasts to an even thickness. Coat the chicken in the Cajun seasoning.
Heat a large oven proof skillet over medium heat and preheat the oven to 350 degrees.
Bring a large pot of water to a boil.
Pour 1 tablespoon of the olive oil into the skillet. Add the chicken breasts and ook for 5 minutes.
Flip the chicken breasts over and cook for 3 more minutes.
Place the skillet in the oven and allow to cook through, about 5 more minutes.
Remove the skillet from the oven and place the chicken on a cutting board to rest.
Add the fettucini to the boiling water and cook until al dente.
While the pasta is boiling, place the skillet back over medium heat and add the remaining tablespoon of olive oil. Stir in the garlic and cook for 1 minute. (You could add in some sun-dried tomatoes here, but my husband would divorce me if I did such a thing.)
Add the heavy cream and butter to the skillet and cook until the butter has melted and it's heated through, stirring often.
While the butter is melting, slice the chicken into bite sized pieces.
Add the cheese to the cream mixture and stir until fully melted and combined.
Drain the pasta and add it to the alfredo sauce. Add in the chicken and toss to coat.
Salt and pepper, to taste.