In a large skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper. Add the chicken to the skillet and cook for about 5-7 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and sauté for about 3-4 minutes until softened. Add the minced garlic and cook for an additional 1 minute until fragrant.
Stir in the diced tomatoes (with their juices), dried basil, and dried oregano. Bring the mixture to a simmer and cook for about 5 minutes.
Lower the heat and pour in the heavy cream, stirring to combine. Add the chopped fresh basil and grated Parmesan cheese, mixing until the cheese is melted and the sauce is creamy.
Return the cooked chicken breasts to the skillet, spooning the sauce over the top. Allow to simmer for an additional 5 minutes to heat through.
Serve the creamy tomato basil chicken over pasta, rice, or with crusty bread to soak up the sauce.