Heat olive oil in a large skillet and cook chicken until golden and cooked through. Remove and set aside.Add garlic and Cajun seasoning to the pan and cook briefly until fragrant.Pour in chicken broth, bring to a boil, and add linguine.Simmer while stirring until pasta is tender and sauce thickens.Stir in cream and cooked chicken, then simmer until glossy.Remove from heat, add Parmesan, adjust seasoning, and serve.