Place the chicken strips in a bowl and toss with the cajun seasoning until evenly coated.
Heat the 12-inch non-stick skillet over medium heat and melt the butter.
Add the seasoned chicken to the skillet and sauté until cooked through and tender, about 5 to 7 minutes.
Stir in the heavy cream, chopped sun-dried tomatoes, dried basil, salt, minced garlic, and black pepper; bring to a gentle boil.
Reduce the heat and simmer the sauce until it thickens slightly, about 2 to 4 minutes.
Toss the hot, cooked linguine with the sauce and chicken until well coated, then serve immediately with optional grated Parmesan.