Chicken Gyros with Tomato Tzike

Sauce
   1 cup plain Greek yogurt
   2 tablespoons finely chopped fresh mint leaves
   1 tablespoon extra-virgin olive oil
   1½ teaspoons fresh lemon juice
   ½ teaspoon kosher salt
   ¼ teaspoon freshly ground black pepper
   1 cup finely chopped tomato
   ½ cup finely diced English cucumber

Marinade
   3 tablespoons extra-virgin olive oil
   3 tablespoons fresh lemon juice
   1 tablespoon dried oregano
   1 garlic clove, minced
   ½ teaspoon kosher salt
   ¼ teaspoon freshly ground black pepper
   ⅛ teaspoon crushed red pepper flakes
Other
   1½ pounds chicken breast tenders
   1 small red onion, cut crosswise into ½-inch slices
   Extra-virgin olive oil
   6 flat breads or pitas

Instructions

   In a medium bowl whisk the yogurt, mint, oil, lemon juice, salt, and pepper. Add the tomato and cucumber and stir to combine.

   In a large bowl whisk the marinade ingredients. Add the chicken to the bowl and toss to coat evenly. Marinate at room temperature for 30 minutes.

   Prepare the grill for direct cooking over medium heat (350° to 450°F).

   Lightly brush the onion slices on both sides with oil. Remove the chicken from the bowl, letting the herbs cling to the chicken. Discard the marinade. Grill the chicken and onion slices over direct medium heat, with the lid closed, until the meat is firm to the touch and the juices run clear, and the onion is tender, 6 to 8 minutes, turning once. Remove from the grill.

   Warm the flat breads over direct medium heat until lightly charred, about 2 minutes, turning once or twice.

   Layer some chicken, sauce, and onion inside the flat breads and serve warm or at room temperature.