Combine all dry seasonings in a small bowl: smoked paprika, brown sugar, salt, garlic powder, onion powder, chili powder, mustard powder, celery salt, black pepper, allspice, cayenne pepper, and cornstarch. Whisk together thoroughly to distribute the spices evenly—this ensures every bite gets consistent flavor. I like to make this blend a few minutes before cooking so the flavors start to meld together slightly.
Cut the chicken breast or thighs into uniform 1-inch cubes—keeping them the same size ensures even cooking. Place the chicken pieces in a bowl or resealable bag, then add the spice blend from Step 1. Toss thoroughly until every piece is evenly coated with the seasoning mixture. I find using a bag makes this easier because you can shake it vigorously to coat all the nooks and crannies of the chicken.
Heat the olive oil in a large skillet over medium-high heat until it shimmers and is hot enough that a piece of chicken sizzles immediately when it hits the pan. Working in a single layer if possible (do in batches if needed to avoid crowding), add the seasoned chicken pieces from Step 2. Cook for 5-8 minutes, stirring occasionally, until the chicken is golden brown on most sides and cooked through (internal temperature should reach 165°F). The browning creates depth of flavor through the Maillard reaction, which makes these bites extra delicious.
Remove the pan from heat and transfer the BBQ chicken bites to a serving platter or bowl. Serve warm as an appetizer, snack, or over salad or rice.