Heat a grill to medium (350° to 400°). In a large, wide bowl, toss chicken with oil, salt, and pepper until evenly seasoned. Grill chicken, covered, turning every 10 minutes or so with tongs, until golden, 25 to 35 minutes.
Set wings top side down. Generously brush with about 1/2 cup barbecue sauce. Grill, covered, about 3 minutes until sauce is somewhat set. Turn wings over and generously brush with another 1/2 cup or so of sauce. Grill, covered, until sauce is somewhat set, 2 to 3 more minutes. Meanwhile, put remaining sauce in a bowl.
Set chicken on a platter and scatter green onions on top. Serve with sauce.