In a small pot, add all the ingredients for the brine. Stir and bring to a boil.
As soon as the brine reaches a boil, remove from heat and set aside to cool for 1 hour. After 1 hour, strain the brine into a bowl to remove the large pieces. Place the cubed chicken in the brine and let them soak for at least 30 minutes or up to 1 hour. While you wait, preheat the oven to 350 ℉.
Strain the chicken and pat dry with paper towels.
In a pan drizzled with olive oil over medium-high heat, add the chicken cubes. Work in batches if necessary. Be sure not to overcrowd the pan. Brown the chicken on all sides and cooked through (about 5-7 minutes).
In a sheet pan covered with foil, place your pita or flatbread and drizzle with a small amount of olive oil and Greek seasoning. Bake for 5-7 minutes or until warmed to your liking.
Remove pita or flatbread from the oven. Spread with hummus and evenly distribute your chicken pieces, red onion, cherry tomatoes, cucumber, and feta cheese. Finish it off by drizzling olive oil and balsamic reduction on top. Serve and enjoy!