In a small bowl, combine ingredients for basil butter; blend well. Place on a sheet of plastic wrap, form into a log and refrigerate until needed.
Preheat gas or charcoal grill, or broil Press black pepper into 1 side of each chicken breast half. In a small bowl, combine melted butter, basil, and salt. Brush each breast half with butter mixture; place on grill and cook, turning until done throughout, about 7 or 8 minutes per side.
When chicken is done, place 1 breast half on each of 4 plates; top with 1/4 of the basil butter log.