Preheat oven to 400°F (200°C).
Scrub the Russet potatoes and pierce them several times with a fork.
Place potatoes directly on the oven rack and bake for 45 to 50 minutes until the skin is crisp and the inside is tender.
While potatoes bake, season the chicken breast with salt and pepper, then pan-sear or poach until the internal temperature reaches 165°F.
Shred the cooked chicken using two forks and set aside.
Remove potatoes from the oven and let them cool slightly; slice each in half lengthwise.
Scoop out the potato flesh, leaving about a 1/4-inch thick shell.
Brush the inside and outside of the potato skins with olive oil and sprinkle with garlic powder.
Place the skins cut-side up on a baking sheet and bake for 10 minutes to further crisp the edges.
Divide the shredded chicken among the four potato halves and top each with a sprinkle of shredded cheddar cheese.
Return to the oven for 5 minutes until the cheese is bubbly and melted.
Finish each potato skin with a dollop of Greek yogurt and a garnish of freshly chopped chives.