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Step 1
Marinate the chicken: Whisk together all ingredients for the marinade in a large bowl or a ziploc bag. Pat chicken dry and coat in marinade. Cover bowl with plastic wrap or seal plastic bag if using, and chill for 30 minutes to an hour.
Step 2
Remove chicken from marinade and shake of any excess. Heat 1 tablespoon olive oil in a large skillet. Over medium high heat, add the chicken and cook until no longer pink, about 3 minutes per side. Remove the chicken from the pan and let rest for 5 minutes. Once rested, thinly slice and set aside in a warm place. Wipe the pan clean.
Step 3
Heat another tablespoon of olive oil in the same pan used for the chicken. Add the red onion, and cook over medium high heat until softened, about 3-4 minutes. Remove from heat and set aside.
Step 4
While the chicken is cooking, stir together cucumber, tomatoes, feta, kalamata olives, parsley, mint, and olive oil in a large bowl until combined. Add salt and pepper to taste. Set aside.
Step 5
In a small bowl, whisk together ingredients for tahini sauce, except for the water. The tahini will get very thick at first. While still whisking, slowly pour in the water to thin it out. Add salt and pepper to taste.
Step 6
Assemble the wraps: Divide the chicken and onion evenly between the two warmed pita. Top with the cucumber and tomato mixture. Drizzle with tahini sauce. Top with any extra fresh mint, parsley, and ground black pepper. Serve immediately.