In a large mixing bowl, stir the salt in water until completely dissolved. Place chicken in brine and refrigerate for 30 minutes.
Preheat oven to 350 degrees (to heat pita). Wrap the pita bread in aluminum foil and seal tightly.
Meanwhile, make the marinade; In a small mixing bowl, whisk together the oil, parsley, lemon zest, lemon juice, honey, oregano, and 1/2 teaspoon black pepper. Pour 1/4 cup into a large mixing bowl (large enough to accommodate cooked chicken later) and set aside.
Remove chicken from brine and pat dry with paper towels. In a large mixing bowl, toss the chicken pieces with the remaining marinade until evenly and well coated. Thread chicken onto skewers.
Place foil wrapped pita in oven and heat until warm, about 10-15 minutes or until warmed through.
Cook chicken skewers on grill or grill pan 5-7 minutes per side, or until chicken is cooked through and registers 160 degrees on an instant thermometer. Using a fork, push hot chicken off skewers and into the bowl with reserved marinade. Toss gently to evenly coat; cover with foil and let sit for 5 minutes.
Assemble the Gyros; Place a pita on a piece of parchment or foil, place a layer of chicken down the center, tzatziki sauce, and veggies. Serve immediately.