Preheat a grill to medium-high heat.
Coat each chicken breast lightly with the olive oil ans season with salt and pepper.
Grill the chicken, flipping once, until the internal temperature reaches 165 degrees 15 to 25 minutes, depending on the thickness of each breast.
When the chicken is almost finished cooking, top each breast with a round of goat cheese, close the grill lid, and allow the cheese to soften, 2 to 3 minutes.
Make the sauce: In a medium-sized saucepan over medium heat, melt 1 tablespoon of the butter. Add the onions and garlic and saute until soft and translucent. Add the lemon juice and wine, stir and simmer until the sauce is reduced by almost half, 4 to 5 minutes.
Cube the remaining 7 tablespoons of butter and add to the sauce, one cube at a time, stirring to allow each cube to melt before adding the next.
Add the sun-dried tomatoes, lower the heat to medium-low, and simmer for 2-3 minutes to reduce the sauce.
Add the basil, toss to combine, and remove from the heat.
Remove the chicken from the grill, plate, and spoon the Tuscan sauce over each breast.