Heat the oven to 350°F. Scrub each potato clean, rinse, and pat dry, then pierce several times with a fork. Arrange them on a baking sheet, drizzle lightly with oil, and season generously with salt all over.
Slide the potatoes into the oven and let them bake for a little over an hour, until they're crisp on the outside and easily pierced with a fork on the inside.
Toward the end of the baking time, add the chopped chicken to a saucepan along with the barbecue sauce. Warm gently over low heat, stirring occasionally, until heated through — about 10 minutes or less. Stir in extra sauce if you'd like it saucier.
Once the potatoes are done, take them out and slice each one open lengthwise, fluffing the inside with a fork. Spoon the barbecue chicken generously over each one — or, for easier serving, chop the potato onto a plate first and top with the chicken.
Finish with cheese, sour cream, and chives as you like, then serve.