Prepare grill for high heat (450° to 550°). Rub 2 boned, skinned chicken breast halves with olive oil and cook, turning once, until no longer pink. Slice.
Meanwhile, whisk 2 tbsp. fresh lemon juice, 1/3 cup olive oil, 1 tbsp. fresh oregano, and 1/2 tsp. freshly ground black pepper; set aside. Boil 1 lb. asparagus (ends trimmed), cut in spears and halved lengthwise, just until bright green; rinse with cold water.
In a bowl, combine reserved chicken; 4 oz. feta cheese, broken into chunks; asparagus; 2 cups halved grape tomatoes; ½ cup pitted kalamata olives; and 2 cups pita chips. Toss gently with reserved dressing. Add 2 cups baby arugula and toss once just to combine.
Print or save recipe: Grilled Chicken Pita Salad