Wrap the chicken in plastic wrap and pound until thin. Remove the chicken from the plastic wrap and pat dry with a paper towel. Season with salt and pepper and brush with olive oil.

Grill the chicken for about 3 to 4 minutes on each side until it reaches an internal temperature of 165°F. Transfer the grilled chicken to a plate and cover lightly with plastic wrap.

Sauté the onions and garlic in 2 tablespoons of butter until the onions are translucent. Add the wine and lemon juice and reduce the heat to a simmer. Stir gently until reduced by half. Add 3 tablespoons of cold butter and whisk until the butter has melted. Turn off the heat and whisk in the remaining 3 tablespoons of butter.

Pour the sauce through a strainer to remove the onions and garlic. Return the sauce to the pan. Add the sun-dried tomatoes and half of the basil and stir.

Place each chicken breast on a plate. Place a piece of goat cheese on the chicken and then spoon the sauce over the chicken. Top each chicken breast with the remaining basil.