Melt butter in large nonstick skillet over medium-low heat. Add leeks; sauté until tender but not brown, about 10 minutes. Add all except one tablespoon of cream to skillet; cook over very low heat until almost all of liquid is absorbed, stirring occasionally, about 10 minutes. Remove from heat and cool.

Preheat broiler. Butter medium broilerproof dish. Stir salmon into leek mixture. Transfer mixture to prepared dish. Pour remaining cream over leek mixture. Broil until top is golden brown, watching closely to avoid burning, about 2 minutes. Sprinkle with chives. Serves 4.