Prepare the pearl onions: Bring a pot of water to a boil. Fill a large bowl with ice water. Add the pearl onions to the boiling water and cook 1 minute. Drain and transfer to the ice water to stop the cooking. Drain again, then slip off the skins.
Combine the turnips, butter, honey, lemon zest, bay leaves, 1 3/4 teaspoons salt and 1/4 cup water in a large nonstick skillet. Bring to a boil over medium heat, then cover and cook until the turnips are just slightly tender, 8 to 10 minutes.
Stir in the parsnips and pearl onions, cover and cook until the vegetables are tender, 8 to 10 minutes. Uncover and simmer, stirring occasionally, until most of the liquid is evaporated, 5 to 7 minutes. Gently toss the vegetables to coat and transfer to a serving dish. Top with the chives.
Prepare the pearl onions (step 1) up to 2 days ahead; refrigerate in an airtight container.