Preheat oven to 400°. Cut garlic heads in half crosswise and wrap tightly in one large piece of foil. Bake until garlic is very soft when pressed and light golden brown (unwrap to test), 45 minutes to 1 hour. When garlic is cool enough to handle, squeeze cloves from skin into a small bowl. Add olive oil, wine, 1 1/2 teaspoons salt, and 1/2 teaspoon pepper; mash garlic with a fork until mixture is smooth.
Meanwhile, in a 6- to 8-quart pan, combine potatoes and 4 quarts water. Cover and bring to a boil over high heat. Reduce heat and simmer until potatoes are tender when pierced, about 20 minutes. Drain and return to pan.
Add garlic mixture and chives to potatoes and stir gently until combined but still chunky. Add more salt and pepper to taste. Let cool completely, then chill airtight for up to 1 day.