In a large skillet over medium heat, melt the butter. Once melted, add the garlic and onion, and saute until soft, about 4 minutes.
Add the white wine and lemon juice and bring the liquid to a simmer. Continue to cook until the liquid has reduce by half, about 8 minutes. Turn the heat of your pan to low and add the butter, one stick at a time. Add the sun dried tomatoes, basil, kosher salt, black pepper and stir until incorporated. Remove from heat and cover with a lid to keep warm.
Preheat your grill or grill pan to medium high heat. Clean and grease the grates. Pat chicken completely dry, then sprinkle with salt and pepper, and press to adhere.
Cook chicken in grill pan or on the grill for 8-10 minutes on each side, until the internal temp of your chicken reaches 165 F.
Place cooked chicken on a plate and divide the goat cheese over each breast. Spoon the sauce on top, and enjoy!