Freeze the bacon on a plate until firm, 20 to 30 minutes (this will make it easier to chop). Dice the bacon and set aside.
Meanwhile, place a pizza stone or inverted baking sheet in the top third of the oven and preheat to 475 degrees F. Brush a large piece of parchment paper with 2 tablespoons olive oil. Stretch the pizza dough into an 11-by-15-inch rectangle on the parchment. Transfer the dough (on the parchment) to a pizza peel or another inverted baking sheet; set aside.
Peel and very thinly slice the potatoes with a mandoline or knife and place in a large microwave-safe bowl. Cover with plastic wrap and microwave until tender, 3 to 4 minutes. Uncover and toss the potatoes with the remaining 2 tablespoons olive oil, 1 teaspoon salt and a few grinds of pepper until fully coated.
Spread the potatoes all over the pizza dough, with a slightly thinner layer in the center. Top with the bacon. Slide the pizza (on the parchment) onto the hot pizza stone and bake until the crust is golden and the potatoes are tender and crisp around the edges, 30 to 35 minutes. Remove from the oven and dot with the cheese, then return to the oven and continue baking until the cheese just melts, 1 to 2 minutes. Sprinkle with chives.
Let your pizza dough come to room temperature (about 30 minutes) before stretching it. If the dough is still difficult to work with, let it sit for a few more minutes.