Whisk together the chicken broth, paprika, garlic powder, onion powder, chili powder, brown sugar, Worcestershire sauce, and liquid smoke in a bowl until combined.
Add the chicken breasts to your Instant Pot. Pour the chicken broth mixture over top.
Close the Instant Pot's lid, set the valve to "sealing", and cook on high pressure for 10 minutes. It will take about 10 minutes for it to get up to pressure.
Once the countdown has finished, let the pressure release naturally for 5 minutes, then carefully do a quick pressure release for the remaining pressure.
Add the chicken to a large bowl and shred it with 2 forks. If you wish, add in a couple of spoonfuls of the liquid left in the Instant Pot. Add your BBQ sauce and toss until coated.
I like to serve the pulled chicken in buns.