Cover the potatoes with water and bring them to a boil in a large stockpot over high heat. Cook until the potatoes are tender, about 30 minutes; drain.
While the potatoes are cooking, render the bacon until crisp in a large skillet over medium-high heat, about 5 minutes. Drain the bacon on several paper towels and break into small, bite-size pieces. Set aside.
Mix the mayonnaise, mustard, barbecue sauce, and hardboiled egg in a large bowl. Slowly add the potatoes to the dressing and let them absorb the liquid, about 15 minutes. Add the celery, red onion, thyme, salt, and pepper and refrigerate until well chilled. Just before serving, garnish with the bacon and chives, if desired.
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