Heat an outdoor grill to high heat. Place salmon on 3 slightly overlapping large sheets of aluminum foil.
In a bowl mix together soy sauce, chili sauce, ginger, garlic, lime juice, lime zest, and brown sugar. Pour the sauce over the salmon. Place salmon in aluminum foil on the grill.
Grill salmon for 4-7 minutes on each side or until fully cooked. Remove and place on a platter. If there is any sauce left over on the aluminum foil, pour it over the fillets.