Season the chicken thighs with salt, pepper, and paprika. This helps build a flavorful base even before the sauce is added.
Sauté mode (or regular sauté) in the Instant Pot: add a splash of oil, then cook the onion until translucent, about 2-3 minutes. Add garlic and cook 30 seconds more until fragrant.
Deglaze the pot with a small splash of chicken broth, scraping up any browned bits from the bottom. This adds depth to the sauce and prevents a burn notice.
Place the seasoned chicken into the pot. Pour in the remaining broth and half of the BBQ sauce. Stir in the apple cider vinegar and brown sugar if using.
Close the lid, set the valve to sealing, and cook on high pressure for 12 minutes (thighs).
Natural release for 10 minutes, then quick release the remaining pressure. Remove the chicken and shred with two forks.
Return the shredded chicken to the pot, stir in the remaining BBQ sauce, and simmer on sauté for 2-3 minutes to meld flavors and lightly thicken the sauce.
Taste and adjust seasoning with salt, pepper, or a touch more BBQ sauce if you prefer it saucier.
Serve immediately, or keep warm in the pot on the warm setting. This pulled chicken is great on buns, over rice, in bowls, or on top of nachos.