Bring a large pot of water to a boil. Meanwhile, in a small bowl, combine the mayonnaise, lemon juice, lemon peel, pickle, chives and hot sauce; cover and refrigerate.
Cut four 10-by-18-inch sheets of heavy-duty aluminum foil. Place each salmon fillet on a sheet and drizzle with olive oil; season with salt and pepper. Fold the foil over the salmon to enclose, then, pressing out any air, fold and press the foil on the cut sides to seal. Carefully drop the packets in the boiling water, cover and cook until the salmon is just firm to the touch, about 10 minutes.
Transfer each packet to a plate and carefully cut open. Dollop the fillets with the tartar sauce.