Cut deboned chicken into bite-size pieces. Season with salt and pepper. Set aside.
Prepare sauce: Mix ketchup, steak sauce, Worcestershire sauce, and liquid smoke. Set aside.
Assemble chicken and peppers on four skewers: thread with one red pepper square, two pieces chicken, then one green pepper square, two pieces chicken, etc., ending with pepper. Baste with sauce. Grill until done, turning once. Baste with sauce while grilling.