Put water and chicken breasts or thighs in the Instant Pot.
Close the Instant Pot and turn the valve to a Sealing position.
Select the "Pressure Cook" or "Manual" setting and set the time for 8 minutes for chicken breasts (or 13 minutes for thighs).
Once it finishes cooking, allow the pressure to release naturally for 5 minutes, then release the remaining pressure using the quick release.
Take the cooked chicken out of the Instant Pot and chop into pieces. Pour the water out of the pot.
Put the Instant Pot on a Saute setting.
Return the chopped chicken back to the pot, add BBQ sauce to it and mix until combined. Cook, stirring, for 1 minute, or until the BBQ sauce is completely warmed through.