Prepare a grill for medium heat; lightly oil the grates.
Season the chicken pieces with salt and pepper and thread onto four 12-inch metal skewers. Grill the chicken, turning often, until just cooked through, 4 to 6 minutes.
Whisk the olive oil, lemon juice and oregano in a large bowl; season with salt and pepper. Add the lettuce, cucumber, olives and red onion and toss until well coated. Divide among 4 plates and top with some of the feta chunks and a chicken skewer. Warm the pita bread on the grill, cut into wedges and serve with the salad.
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