Season the chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium heat. Once hot, add the chicken breasts and sear for about 5-6 minutes on each side, until golden brown and cooked through. Remove them from the skillet and set aside.
In the same skillet, add the chopped onion and sauté for about 3 minutes until soft. Add the minced garlic and cook for another minute, until fragrant.
Pour in the crushed tomatoes, stirring to combine, and let the mixture simmer for 5 minutes.
Lower the heat and stir in the heavy cream, chopped basil, Italian seasoning, and balsamic vinegar. Let it simmer for another 2-3 minutes, allowing the sauce to thicken slightly.
Return the chicken to the skillet and coat it well with the creamy tomato basil sauce. Sprinkle the grated Parmesan cheese over the top.
Allow everything to cook together for about 3-5 minutes, until heated through. If desired, add red pepper flakes for a touch of heat.
Serve hot, garnishing with additional fresh basil if desired.