Combine first 5 ingredients in a small skillet; cook over medium heat until reduced to 3 tablespoons. Stir in whipping cream, and cook until reduced to 3 tablespoons.
Reduce heat to medium-low; add butter, 1 tablespoon at a time, stirring until butter melts. Remove from heat; strain through a metal sieve. Stir in lime zest and salt. Keep warm. Stir in chives just before serving.