If you use bamboo skewers, be sure to soak them in water before grilling for at least 30 minutes. It'll prevent them from catching on fire.
In a blender, puree onion, tomatoes, lemon juice, oregano, garlic, 1 Tbsp. oil, 1 tsp. salt and 1/2 tsp. pepper. Transfer to a ziplock bag and add chicken; seal and shake. Refrigerate for at least 2 hours, turning bag once or twice.
If using bamboo skewers, soak in water for at least 30 minutes. Preheat grill to medium-high. Remove chicken from marinade (discard marinade) and thread on skewers, about 3 pieces each. Oil grill grates. Grill kebabs, turning, until lightly charred on outside and cooked through, 10 to 15 minutes.
Place kebabs on warmed pitas with cucumber and a dollop of yogurt. Season with additional salt and pepper, if desired; serve.