In colander, toss cucumber, radishes and sugar with 1 tsp. salt; let sit 10 minutes. In bowl, whisk 2 tbsp. EVOO with vinegar; season dressing. Brush chicken with remaining 1 tbsp. EVOO. In large skillet, cook chicken over medium until cooked through, 8 to 10 minutes per side; slice. Top pitas with hummus, chicken, cucumber mixture, tomatoes and parsley; drizzle with dressing.
Quick Hack for Cutting Cherry Tomatoes