Add the bbq sauce to a slow cooker, and turn on high heat while preparing the chicken.
In a frying pan, add olive oil, and heat over medium high heat. Add chicken breasts, and season liberally with salt and pepper. Brown both sides of the chicken, but don't cook through.
Add chicken to the crockpot. I allow it to stay on high heat until the BBQ sauce has begun to bubble, then I turn it on low for 3-4 hours. You can cook it on low the entire time if you'd prefer.
Cooking the chicken on high is fine (for 1 1/2-2 hours), but the chicken doesn't stay as moist.
Once chicken is cooked through and very tender, take the chicken breasts out, and shred them with 2 forks. The chicken should come apart very easily. Add the chicken back to the sauce in the crock pot, and mix well. Turn off the heat after shredding the chicken to avoid it drying out.
To make the slaw, add shredded veggies to a bowl. After cutting apples, add to a dish with lemon juice and some added water to keep from browning.
Add the ingredients, apple cider vinegar down, to a jar, and shake well. Drain the apples, and add to the slaw ingredients, then toss the slaw with the dressing to coat well.
The slaw can be made a day ahead of time if needed, but I prefer it on the first day while it's still crisp.
Layer shredded chicken and apple slaw on buns. We found that no other condiments were necessary with the flavorful sauce and the dressing on the slaw.