Position an oven rack in the center of the oven. Preheat the oven to 375 degrees F.
For the fish topping: Mix the chives, parsley and lemon zest in a small bowl. Cover and chill. This can be prepared 4 hours ahead, but keep chilled.
For the baked halibut: Coat the halibut fillets all over with the olive oil. Place the fish on a rimmed baking sheet. Sprinkle with the salt, pepper and chive-lemon topping, pressing slightly to adhere. Bake the fish just until opaque in the center, 9 to 10 minutes. Transfer 1 fish fillet to each of 4 plates. Spoon the Arugula Salsa Verde alongside. Serve with the lemon wedges, if using.
Stir the arugula, parsley, olive oil, capers, lemon juice, lemon zest, salt and red pepper together in a small bowl. Cover and chill. The salsa can be prepared 4 hours ahead, but let it stand at room temperature 1 hour before serving.