Season chicken breasts with salt and pepper, and place in a pot over high heat with onion, seasonings, apple cider vinegar, and barbecue sauce.
Add just enough water to almost cover the chicken (about 1/2 cup). Bring water to a boil. Reduce heat and simmer until the chicken is cooked through, about 10-15 minutes. Remove the chicken from the sauce and shred with 2 forks.
Continue to boil the sauce, stirring occasionally until reduced and thickened (about 10-15 minutes.) Add the shredded chicken back into the sauce and divide mixture between the four buns just before serving.