In a small saucepan, add wine and lemon juice. Bring to a simmer. Cook for about 10 minutes, until the liquid has reduced.
Add 6 tablespoons butter, sun dried tomatoes, and basil to the pan. Keep on low until butter has melted.
Season chicken with salt and pepper.
In a large skillet, add the remaining 2 tablespoons of butter on medium-low heat. Add onion and garlic. Cook until onion is translucent, about 5 minutes.
Add chicken breasts. Cook on each side for 10 minutes, or until chicken is cooked all the way through and internal temperature registers 165 F.
Remove chicken from skillet. Using a small spoon, top with goat cheese. Top with lemon wine sauce.