Lay onions in a large skillet, trimming top of dark greens to fit. Add 2 tablespoons butter and 1/2 cup water to skillet; season with salt. Bring to a boil; cover. Reduce heat and simmer onions until greens are soft and bulbs are almost tender, 15-20 minutes. Uncover and cook, turning onions occasionally, until bulbs are completely tender, 5-8 minutes longer.
Transfer onions to a plate. Simmer cooking liquid in skillet until reduced to 2 Tbsp., about 1 minute. Remove from heat and whisk in remaining 2 tablespoons butter. Return onions to skillet and turn to coat with sauce. Top with fresh chives.