In a mixing bowl whisk together 1 cup barbecue sauce, 1/2 cup sweet tea, 1 tsp garlic powder, 1 tsp onion powder, and 1/2 tsp salt until smooth.
Divide the sauce into two roughly equal portions (about 3/4 cup each).
Trim any excess fat from the chicken thighs and place them in the slow cooker in a single layer.
Pour one half of the sauce over the chicken, then spread the thinly sliced onion on top.
Cook on high for 3–4 hours or on low for 4–6 hours, until the chicken is fully cooked and tender.
Carefully remove the chicken from the slow cooker and strain the onions from the cooking liquid.
Shred the chicken with forks or tongs, then toss it with the strained onions and the remaining half of the sauce until well combined.
Serve the pulled chicken on sandwich buns with a leaf of butter lettuce, or serve on its own.