Preheat the oven to 400° and line a rimmed baking sheet with aluminum foil. In a small bowl, stir together the mustard, olive oil and chives.
Season the salmon fillets with salt and pepper and place them skin side down on the prepared baking sheet. Spread the mustard mixture over the tops of the fillets. Roast the fish for 6 minutes.
Preheat the broiler. Broil the salmon 6 inches from the heat for about 4 minutes, until the mustard crust is browned and the salmon is almost cooked through. Using a spatula, carefully slide the salmon fillets off their skins and transfer to plates; leave the skin on, if desired. Serve immediately.