Prepare the Chicken.Preheat your oven to 375°F (190°C).
In a small bowl, mix the chèvre cheese, parsley, chives, and minced garlic. Season with salt and pepper. Using a sharp knife, create a pocket in each chicken breast by slicing horizontally through the thickest part, being careful not to cut all the way through.
Stuff each chicken breast with the chèvre mixture and secure with toothpicks if necessary.
Cook the Chicken. Heat the olive oil in a large oven-safe skillet over medium-high heat.
Sear the stuffed chicken breasts for 3-4 minutes on each side until golden brown.
Transfer the skillet to the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through and the internal temperature reaches 165°F (74°C).
Prepare the Herbed Cream Sauce. While the chicken is baking, melt the butter in a saucepan over medium heat.
Add the chopped shallot and cook until softened, about 2-3 minutes.
Stir in the heavy cream and chicken broth, bringing the mixture to a simmer.
Add the fresh thyme and basil, and season with salt and pepper to taste.
Continue to simmer the sauce until it thickens slightly, about 5-7 minutes.
Serve. Remove the toothpicks from the chicken breasts and place them on serving plates.
Spoon the herbed cream sauce over the chicken and garnish with additional fresh herbs if desired.
Serve with your favorite side dishes, such as roasted vegetables or a fresh salad.