Preheat the oven to 400° and butter a shallow 9-by-13-inch baking dish. In a medium saucepan, bring the heavy cream and milk to a simmer. Whisk in the garlic, chipotles and adobo sauce and season with salt and pepper. Keep warm.
Using a mandoline, slice the potatoes crosswise 1/8 inch thick. Arrange one-fourth of the potato slices in the prepared baking dish, overlapping them slightly. Sprinkle 1/4 cup of the cheese and 1 tablespoon of the chives over the potato slices. Repeat the layering two more times. Top with a final layer of potatoes and the remaining 1/4 cup of cheese. Pour the cream mixture over and around the potatoes.
Bake for about 25 minutes, until the potatoes are tender and bubbling and the top is golden brown. Let stand for 15 minutes. Sprinkle with the remaining 1 tablespoon of chives and serve.
Make Ahead The unbaked gratin can be refrigerated overnight. Return to room temperature before baking.