For the Chicken

1. One at a time, place the chicken breasts in a 1-gallon zip-lock bag; using a meat mallet, pound to an even ½-inch thickness. (Skip this step if using chicken tenderloins.) Cut the meat into 2-inch chunks.
2. Mix all the ingredients except for the chicken together in a large bowl. Add the chicken pieces to the bowl and stir until evenly coated. Cover with plastic wrap and let the chicken marinate in the refrigerator for at least 4 hours or overnight.
3. Thread the marinated chicken onto skewers, folding if the pieces are long and thin. Be sure not to cram the skewers. (Note: You'll need about 6 skewers.)
4. Preheat the grill to medium-high heat and, using tongs, dip a wad of paper towels in vegetable oil and carefully wipe the grill grate several times to prevent sticking. Place the skewers on the grill and cook, covered, turning to brown evenly, until the chicken is cooked through, 5 to 7 minutes total. Transfer the chicken to a platter and cover to keep warm. Meanwhile, briefly grill the pita bread until warmed through. Serve with tzatziki sauce, warm pita, and lemon wedges.

For the Tzatziki

1. Combine all of the ingredients in a medium bowl and mix until well combined. Taste and adjust seasoning if necessary. Cover and chill for up to 2 days or until ready to serve.
2. Note: If using wooden skewers, soak them in water for 30 minutes prior to using to prevent them from burning on the grill.
3. ALTERNATIVE BROILER & GRILL PAN COOKING INSTRUCTIONS:
4. To use a broiler: Preheat your broiler to high. Arrange an oven rack so that the skewers will be 5 to 6 inches away from the broiler element. While the broiler is heating, line a baking sheet with aluminum foil for easy cleanup. Place a wire rack on the baking sheet and spray the rack with nonstick cooking spray. Arrange the skewers on the wire rack. Once the broiler is preheated, broil the skewers for 3 to 4 minutes. Using a pair of tongs, turn the skewers over, and cook for another 3 to 4 minutes or until the chicken is fully cooked and has a nice golden color.
5. To use a grill pan: Heat the pan over medium-high heat on the stove. Once the pan is hot, brush it lightly with vegetable oil to prevent sticking. Place the skewers in the pan in a single layer (you may need to do this in batches). Cook the skewers for 3 to 4 minutes, then use tongs to turn them over and cook for another 3 to 4 minutes. Continue to turn the skewers, if necessary, until the chicken is fully cooked and all sides have nice grill marks.