Prepare chicken by wrapping in plastic wrap and pounding out until thin. Remove chicken from plastic wrap and pat dry with a paper towel. Season chicken with salt and pepper and brush with olive oil.
Cook chicken on a grill until it is done - it should take 3 to 4 minutes on each side. When chicken is done, place chicken on a plate, and cover lightly with plastic wrap. Slice the goat cheese into four slices and shape the cheese into disks, one for each piece of chicken.
Sauté the onions and garlic in 2 tablespoons of butter until they are fragrant and the onions are translucent. Add wine and lemon juice to pan and simmer gently until it has reduced by half. When the wine has been reduced by half, add 3 tablespoons of cold butter and whisk until the butter has melted completely.
Turn off the burner, add remaining butter and whisk in. The sauce should be getting thick now. Pour sauce through a strainer to strain out the onions and garlic. Then return the sauce to the warm pan and stir in half of the basil. Add sun-dried tomatoes.
Assembly of the final dish
Place each chicken breast on to a plate. Place a piece of goat cheese on the chicken and then spoon sauce over the chicken. Top each chicken breast with the remaining basil.