In a bowl, combine the minced garlic, Greek seasoning blend, olive oil, and salt and pepper. Mix well.
Add the chicken breasts to the bowl and toss until they are well coated in the marinade. Cover and refrigerate for at least 1 hour, or overnight for best flavor.
Preheat the grill to medium-high heat. Remove the chicken from the marinade and grill for 6-8 minutes per side, or until cooked through and juices run clear. Remove from the grill and let rest for a few minutes before slicing into thin strips.
While the chicken is resting, make the tzatziki sauce by combining the Greek yogurt, chopped dill, lemon juice, and salt and pepper in a bowl. Mix well.
To assemble the gyros, warm the pita breads on the grill or stovetop. Spread a generous amount of tzatziki sauce on each pita. Top with shredded lettuce, diced tomatoes, sliced red onion, and grilled chicken strips.
Fold the pita in half and serve immediately. Enjoy your delicious homemade Greek chicken gyros!