30 min (Quick)
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In a large high-sided pot, add the chicken, salt and broth. Cover and bring to a boil, and reduce the heat and simmer until done, about 20 minutes. Remove from heat and allow to cool enough to handle.
With two forks, shred the chicken right in the pot, by pulling the pieces apart. Add the barbecue sauce, reheat the mixture and reduce the liquid if needed, or add some additional chicken broth if too dry. Split the rolls and mound about 1 tablespoon of the chicken on each bottom half; top with the remaining half. Using a toothpick, secure a pickle on top and serve warm.