Place chicken and Cajun seasoning in a bowl and toss to coat.
Heat a large heavy-duty skillet to medium-high heat. Add butter and olive oil to skillet and heat until butter is melted.
Add chicken to skillet and cook on high until chicken is cooked through and crispy, about 6-7 minutes.
Reduce heat to medium and add bell peppers and minced garlic and sauté for 1-2 minutes.
Add heavy cream and simmer for 1-2 minutes. Taste and add salt and pepper to taste.
Turn off heat and toss in the zucchini noodles.