Rub chicken breasts on all sides using 2 tablespoons olive oil. Sprinkle with half of the salt and black pepper.
Place chicken on thegrill and cook without moving for 3 minutes or until the edges begin to turnwhite. Turn the chicken one-quarter turn and continue to cook an additional 2to 3 minutes. Flip the chicken and for 3 minutes before turning one-quarterturn and cook until the chicken reaches an internal temperature of 165 degrees.Allow the chicken to rest for at least 5 minutes.
In a medium saucepan, melt 2 tablespoons of butter. Add the onions and garlic and cook until tender.
Add the wine and lemon juice to the saucepan. Bring to a boil and reduce heat to medium-low. Simmer the sauce for 10 minutes.
Slowly, add the butter about a tablespoon at a time, stirring until melted between each addition.
Stir in sun-dried tomatoes and basil. Remove from heat.
Slice goat cheese and place a disc of cheese over each piece of the grilled chicken. Spoon the sauce over the goat cheese.