In a large pot of salted water, bring the potatoes to a boil. Cook until tender, about 30 minutes. Drain; reserve the pot.
Meanwhile, in a small saucepan or a microwave, heat the half-and-half until steaming. Remove from the heat and stir in the butter until melted. Keep warm.
Using a sieve or food mill, press the potatoes, a few pieces at a time, into the empty pot. Whisk the cream mixture into the potatoes and heat over low heat until warm. Season with salt and pepper. Spoon into a serving bowl and top with the chives.