Combine olive oil, lemon juice, salt, oregano, garlic powder, and pepper in a large resealable bag. Add chicken cubes, mix well, and allow to marinate in the refrigerator 3 hours or overnight.

Pour chicken and marinade into a frying pan over medium-high heat. Cook until chicken is no longer pink in the center and the juices run clear, 10 to 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Stuff each half of pita pocket bread with chicken, onion, tomato, and yogurt; serve while still hot.