Run vegetable peeler down length of carrots, shaving off long ribbons (you will need about 8 cups ribbons). Cook in large saucepan of boiling salted water 2 minutes. Drain and gently pat dry. (Can be made 6 hours ahead. Cover; chill.) Stir orange juice and sugar in heavy large skillet over medium-high heat until sugar dissolves. Boil until reduced to scant 1 cup, about 5 minutes. Add carrots and butter; simmer until carrots absorb most of orange syrup, about 4 minutes. Add honey and vinegar. Mix gently. Season with salt and pepper. Transfer carrots to serving bowl. Sprinkle with chives.
