Pour 1/2 cup of Dr. Pepper into the pot of the electric pressure cooker. Place the chicken thighs over the Dr. Pepper.
Stir together the remaining Dr. Pepper and barbecue sauce. Pour over the chicken thighs.
Cover the electric pressure cooker and set the valve to sealing. Program for manual or “pressure cook” for 20 minutes.
When the cooking cycle is complete, allow the electric pressure cooker to naturally release the pressure for 10 minutes before a quick release of the remaining pressure.
Carefully remove the chicken from the pot and using two forks, shred the chicken, removing any bones.
Add about 1 cup of the sauce from the pot to the chicken, coating the chicken but not making it soupy.
Serve with baked potatoes, buns, sliders, or as it is.