Preheat your oven to 425°F. Scrub the russet potatoes under cold water to remove any dirt, then prick each potato several times with a fork to allow steam to escape during baking. This prevents them from bursting and helps them cook evenly. Arrange the potatoes directly on the oven racks (place a baking sheet on the rack below to catch any drips) and bake for 55-60 minutes until a knife easily pierces the center. The potatoes should be tender but still hold their shape.
While the potatoes bake, combine the chicken chunks, BBQ sauce, brown sugar, cider vinegar, garlic powder, liquid smoke, and smoked paprika in a slow cooker. Stir well to coat the chicken evenly with the sauce and spices. Cook on high for 3.5 hours, stirring occasionally if possible. The chicken should be very tender and easily shredded with a fork. I like to use liquid smoke in moderation—it adds authentic BBQ flavor without overpowering the dish, so don't be tempted to add more than called for.
Once the chicken has cooked through and is tender, use two forks to shred it directly in the slow cooker, breaking it into bite-sized pieces. Turn the slow cooker to high and cook for an additional 10 minutes, stirring occasionally. This allows the shredded chicken to absorb more of the BBQ sauce and develop deeper flavor. The chicken should be moist but not swimming in liquid.
While the chicken finishes cooking, shred the cheddar cheese from the block (pre-shredded cheese doesn't melt as smoothly due to anti-caking agents), and chop the fresh chives. Have the sour cream and butter ready at the table or work area. This mise en place ensures everything comes together quickly once the potatoes are done.
When the potatoes are fully cooked and tender, remove them from the oven and let them cool for 1-2 minutes until they're comfortable to handle. Cut each potato in half lengthwise and gently fluff the interior with a fork. Top each potato half with a pat of butter, then add a generous scoop of the shredded BBQ chicken from Step 3. Sprinkle with shredded cheddar cheese, add a dollop of sour cream, and finish with fresh chives. Serve immediately while everything is hot and the cheese is still melting.