In a medium saucepan set over medium heat, add the beef and cook, stirring occasionally, until the beef is browned and cooked through, about 10 minutes. Drain off and discard any excess fat and return the pan to the heat.
Stir in the ketchup, brown sugar, Worcestershire and mustard, reduce the heat to medium-low and cook, stirring occasionally, for 20 minutes. Pour in the apple juice and stir to combine. Cook, stirring occasionally, until the liquid is reduced by half, about 20 minutes. Season with the salt and pepper.
To serve, add a bun half, cut side up, to each plate. Top each bun with the sloppy Joe mixture and serve, open-faced, with potato chips.