Slice the carrots into 3-inch long by 1/4-inch wide strips. Bring a small pot of water to a boil over medium heat and add the carrots. Cook the carrots until just tender, about 2 minutes. Drain. Stack the carrots into bundles and tie each bundle with a blanched chive.
In a medium saucepan, melt the butter over medium heat. Add the brown sugar and stir until dissolved. Stir in white wine and simmer for 2 minutes. Add the carrot bundles to the sauce and cook until coated with the sauce, about 3 minutes. Transfer to a serving bowl and serve.