Heat grill to medium-high heat. Alternatively, heat a nonstick skillet or grill pan over medium-high heat. Brush the grill grates or pan with oil to keep the burgers from sticking.
Place the ground chicken into a large mixing bowl and add the salt, pepper, garlic powder, ¼ cup barbecue sauce, and diced cheese. Mix together until just combined and ingredients are evenly distributed, being careful to not overmix the chicken.
Divide the meat mixture into 4 equal portions and shape it into patties that are slightly larger than the bottom of a hamburger bun. Place a thumbprint into the middle of each burger, to help prevent shrinkage and even cooking.
Grill or cook for 5 minutes. Flip the burgers, and continue to cook for 5-7 minutes, or until the chicken burgers reach 160 degrees F.
Remove the burgers to a plate and brush with additional barbecue sauce. Tent with foil and allow to rest for 5-10 minutes before serving. This will allow the burgers to reach 165 degrees F.
Serve the burgers on buns with coleslaw or as desired.
To smoke chicken burgers: Preheat Smoker to 300 degrees. Add in chips and let smoke for 5 minutes. Smoke burgers for approximately 40 minutes, or until they reach an internal temperature of 160 degrees. Remove burgers and baste with barbecue sauce and tent. Rest for 10 minutes, to reach 165 degrees, and then serve. To Make Your Own Ground Chicken: Cut boneless, skinless chicken breasts (or chicken thighs) into chunks. Place chicken into the food processor with 1 to 2 ice cubes. Pulse a couple of times, until the meat begins to break down. Be careful to not over-process. It should only take 5-6 pulses to make ground chicken at home.