Preheat the oven to 425F. Line a large baking sheet with parchment paper.
Marinate the chicken: Make the marinade in a medium bowl by whisking together salt, pepper, pressed garlic, dried oregano, lemon juice and olive oil. Add the chicken cubes and let sit in the bowl while you prep the other ingredients.
Once prepped, add the chopped red and orange peppers and halved potatoes to the parchment lined baking sheet. Season with 2 tbsp olive oil, 1 tsp salt and 1/2 tsp pepper. Toss to coat everything evenly.
Next, thread the chicken onto the skewers, you'll have 4-6 skewers. Nestle the chicken skewers in the middle of the pan and move the potatoes and peppers a bit to the side.
Bake everything together for 25-30 minutes until chicken is cooked through and peppers are starting to turn golden.
Use a large cutting board or sheet pan and line with parchment paper. Assemble the vegetables, tzatziki and pitas around the edges of the board or sheet pan, leaving a spot in the middle for the cooked chicken skewers. Season the cucumber and tomatoes with a big pinch of salt. Serve family style (reference the recipe photos for serving inspiration!)