In a small bowl combine goat cheese, Monterey Jack cheese, chives, and basil. Set aside.
Place sweet peppers on the rack of an uncovered grill directly over medium-hot coals. Grill about 8 minutes or until peppers are crisp-tender and starting to brown, turning once halfway through grilling. Remove peppers from grill.
Spoon cheese mixture into sweet pepper pieces; return to grill. Grill for 2 to 3 minutes more or until cheese is melted. Makes 4 servings.