Cook rutabagas in large pot of boiling salted water 2 minutes. Add carrots and cook until vegetables are tender, about 6 minutes. Drain.
Melt butter in large pot over medium-high heat. Add lemon juice, honey, and peel. Bring to boil. Add vegetables; cook until glazed, stirring occasionally, about 6 minutes. Season to taste with salt and pepper. Remove from heat. Mix in fresh chives.