Position an oven rack in the top of the oven and preheat to 450 degrees F. Line the bottom of a roasting pan with parchment paper.
Put the potatoes in a large bowl, sprinkle with 2 teaspoons of the oil, the rosemary and 1/4 teaspoon salt and toss to combine. Arrange the potatoes in a single layer in the pan and roast until the potatoes just begin to soften slightly, stirring as needed, 25 to 30 minutes.
Meanwhile, sprinkle the chicken breasts with 1/2 teaspoon salt and 3/4 teaspoon pepper. Heat the remaining 1 teaspoon of oil in a large nonstick skillet over medium-high heat. Cook the chicken skin-side down until just golden, 4 to 5 minutes.
Set the chicken skin-side up on the partially roasted potatoes. Roast until an instant-read thermometer inserted in the thickest part of the meat reaches 160 degrees F and the juices run clear, 25 to 30 minutes.
Transfer the chicken and potatoes to a platter and serve.