Place chicken thighs in a large Dutch oven or stock pot half-filled with water or with enough water to cover all the chicken. Bring water to a full boil and leave to simmer on medium low heat for 1-2 hours.
After the chicken is done boiling, turn off the heat and remove the chicken to a separate dish to allow the chicken pieces to cool enough to be handled (about 20-30 minutes).
While the chicken is cooling, roughly chop the bell pepper and the onion. Big chunks are okay here. Set aside until we shred the chicken.
Remove the chicken skin and throw away or feed to a pet. Now take the meat off the bones and use two forks to shred the meat. Place shredded meat into a 13×9 baking dish.
Add in the chopped veggies here! Now grab your favorite BBQ sauce and pour that over the top of everything. Mix it all up making sure all the chicken and the veggies are nicely coated.
Next get some aluminum foil and cover tightly. Cook in a 325ºF oven for about 1 hour and 15 minutes to let that wonderful barbecue sauce work its magic.
Serve on your favorite rolls. I prefer mine on an onion roll.
(I have also served this on top of tortilla chips with shredded cheddar cheese on top.)