Preheat the oven to 400 degrees F (200 degrees C).

Slice potato very thinly, about 1/8-inch thick. Place slices in a bowl of water to prevent browning.

Fold parchment paper in half to create two 15x12-inch rectangles. Drain potatoes and arrange 1/2 of the slices on the inside fold of the parchment paper in an overlapping semicircle. Season with salt and pepper. Top with 5 basil leaves and 1/2 of the onion slices. Repeat with the second piece of parchment paper.

Place chicken legs over the onion slices, sprinkle with salt and pepper, and top with pesto. Carefully fold the parchment paper around the chicken, starting from one end, to create sealed packets. Transfer packets to a baking sheet.

Bake in the preheated oven until juices run clear, about 1 hour 10 minutes. Transfer packets to plates and let rest for 5 to 10 minutes before opening and serving.