Mediterranean Chopped-Chicken Pita

Preheat grill to medium-high. Brush chicken with oil; season with salt and pepper. Brush grates with oil. Grill chicken, turning once, until cooked through and lightly marked in spots, 6 to 8 minutes. Transfer to a cutting board. When cool enough to handle, cut into strips.

Brush both sides of each pita with oil. Grill, flipping once, until lightly marked and crisp, 4 to 5 minutes. Spread hummus on one side of each pita. Top with chicken, tomatoes, scallions, radicchio, and feta. Drizzle with oil; serve immediately with lemon.