Place chicken in a large pot of boiling water.  Boil for about 40 minutes, or until chicken is cooked through and it shreds. You should have about 2 cups shredded (1/2 cup per sandwich)

Shred carrots until you have 1 cup.

Combine chicken, carrots and 1/2 cup barbecue sauce in a bowl.

Spread 1/2 tablespoon ranch dressing on each bun.

Top with the chicken mixture and lettuce.

Serve with the broccoli and remainder of the ranch dressing for dipping and clementines.