Season the chicken breasts with salt and pepper.
In a large skillet, heat olive oil and butter over medium heat.
Add chicken and cook until golden brown on both sides and cooked through. Remove and set aside.
In the same skillet, add garlic and sauté until fragrant.
Pour in chicken broth and bring to a simmer.
Add heavy cream and stir until well combined.
Stir in mozzarella and Parmesan until melted and smooth.
Add chopped basil and season with more salt and pepper if needed.
Return chicken to skillet and spoon sauce over the top.
Simmer for a few minutes until everything is heated through. Serve warm.