01 - Sprinkle both sides of the chicken breasts evenly with salt and black pepper.
02 - Melt butter with olive oil in a large skillet over medium-high heat. Add chicken breasts and cook for 6 to 8 minutes per side, until golden brown and cooked through. Transfer to a plate and keep warm.
03 - In the same skillet, add the chopped onion and minced garlic. Sauté for 2 to 3 minutes, stirring occasionally, until softened and fragrant.
04 - Pour in chicken broth, scraping up any browned bits from the bottom of the pan. Allow the liquid to simmer for 2 minutes.
05 - Reduce the heat to medium. Stir in heavy cream, parsley, chives, basil, and thyme. Simmer gently for 3 to 4 minutes until the sauce thickens slightly.
06 - Return the chicken breasts and any accumulated juices to the skillet. Spoon the sauce over the top and simmer for 2 to 3 minutes until heated through.
07 - Garnish with additional fresh herbs if desired and serve warm.