Make the chicken marinade. In a mixing bowl, combine 1/2 cup of the yogurt, the lemon zest, half (about two tablespoons) of lemon juice, the oregano, garlic powder, cumin, coriander, paprika, and 1/4 teaspoon of salt. Stir well to combine. Set this aside.
Cut the chicken breasts in half horizontally to make thin cutlets. NOTE: see the link in the instructions above if you're unsure how to do this. Place each cutlet between two sheets of plastic wrap and pound them gently so each piece of chicken is evenly thick. If you plan to skewer the chicken, cut each cutlet in half lengthwise into strips. Place the chicken in the yogurt marinade. Stir it well to coat everything. Cover and refrigerate for at least one hour or up to overnight.
While the chicken marinates, grate the cucumber and make the tzatziki sauce. Grate about 2/3 of the cucumber into a bowl using a cheese grater. You can peel it if you like, but it's not necessary. Sprinkle the grated cucumber with a pinch of salt and let it sit for about 15 minutes. Place the grated cucumber in a mesh strainer and press out as much water as possible. Alternatively, you can use your hands to squeeze out the water.
Combine the drained, grated cucumber with the remainder of the Greek yogurt and lemon juice. Add dill and minced garlic. Mix well to combine. Season with a pinch of salt or to taste. Set the tzatziki sauce in the refrigerator until ready to serve.
Thread the chicken onto skewers.Heat a grill to high heat, spray the grill grates, and grill chicken for about 10-14 minutes or until cooked through. Flip the chicken after five minutes so both sides cook evenly. Let the chicken cool for a few minutes, and remove it from the skewers if desired.
Slice the remainder of the cucumber into thin slices. In a mixing bowl, combine the cucumbers, red wine vinegar, sliced tomatoes, chopped parsley, and chives. Toss lightly and sprinkle the crumbled feta cheese over the salad.
To serve, warm the pita bread a microwave until soft and pliable (about 15-20 seconds per slice). Top each piece of pita bread with chicken, tomato-cucumber salad, and a dollop of yogurt tzatziki sauce.
Notes
If desired, skip the skewers and grill the chicken flat on the grill.After the tzatziki sauce sits in the refrigerator, some water will separate. Drain this off for a thicker sauce or stir it back in.Refrigerate leftover chicken and tzatziki sauce for up to 2 days. You can also reserve and refrigerate the tomato-cucumber salad, but it will wilt.