Method:
In a large bowl, combine chicken, garlic, pepper, 2 tablespoons oil, 1/2 teaspoon salt and all but 1 tablespoon of lemon juice and toss to coat. Marinate at least 20 minutes or up to 8 hours.
Meanwhile, place cucumbers in a food processor and pulse until finely chopped but not pureed. Transfer to a bowl and stir in feta, onion, parsley, lemon zest, remaining 1 tablespoon lemon juice, remaining 1 tablespoon oil and remaining 1/4 teaspoon salt. Cover and refrigerate up to 8 hours; bring to room temperature before serving.
Prepare grill for medium-high-heat cooking. Thread chicken on metal (or well-soaked wood or bamboo) skewers and grill, turning frequently, until browned and cooked through, 6 to 8 minutes. Remove chicken from skewers, place on a platter and spoon feta-cucumber relish over top.