Make the brine. Add salt and water to a mixing bowl and stir until salt is fully dissolved.
Brine the chicken. Submerge the chicken breasts in the brine. Leave the bowl with the chicken at room temperature for 30 minutes.
Remove the chicken from the brine and drain. Pat dry with paper towels and cut into 4 cm (1½-inch) cubes.
Add chicken, dried oregano, onion powder, paprika, freshly ground pepper, and a generous drizzle of olive oil to a mixing bowl and toss to combine.
Marinate. Let chicken marinate at room temperature until the grill gets heated. Alternatively, cover the bowl and place it in the fridge for a couple of hours or overnight. Make sure to remove from the fridge 30-45 minutes before cooking.
Heat a grill pan or griddle over medium-high heat or a gas grill over moderate heat. Brush lightly with oil.
Thread the meat on the skewers alternately with a piece of vegetable (green, red pepper, and onion).
Grill for about 5-6 minutes on each side. Turn the Souvlaki to grill on all sides until the internal temperature registers 166°F / 74°C on an instant-read thermometer. See Notes Below. Make the Ladolemono. Let the skewers rest on a plate while you prepare the Ladolemono. In a small bowl whisk to combine the lemon juice and extra virgin olive oil.
Drizzle Ladolemono over the skewers and then sprinkle with some dried oregano.
Serve with preferred sides and enjoy!