A well-greased grill basket can be used to keep fillets intact. Or place on non-stick or greased foil with a few holes poked in it for juices to run off.
Season salmon fillets with salt and pepper.
Stir together BBQ sauce and ginger. Divide the mixture in half (two 1/4 cup portions).
Place salmon on an oiled, preheated charcoal or gas grill over medium heat. (If grilling fillets, place skin side down and remove skin after cooking.) Brush salmon with 1/4 cup of BBQ sauce with ginger. Grill uncovered for 4 to 6 minutes per 1/2 inch of thickness. Continue to cook until fish is opaque and separates when tested with a fork.
To serve, place cooked salmon on serving platter or plates. Brush remaining 1/4 cup BBQ sauce with ginger. Sprinkle with chives or green onion. Serve with rice, if desired.