Make the Pita Chips: Preheat the oven to 400 degrees Fahrenheit and place pita wedges on a baking sheet. Season with za'atar, cumin, salt and pepper and drizzle with olive oil and toss to combine.
Bake the pita chips for about 12-15 minutes until toasted, then remove and set aside.
Roast Chicken Breast: Season the chicken breast with turmeric, cumin, za'atar and salt and pepper. Drizzle with olive oil and coat everything evenly all over chicken.
Roast the chicken breasts in the oven at 400 degrees Fahrenheit for about 20 minutes, or until fully cooked through. Remove the chicken from the oven and let cool slightly, then shred the chicken and set aside.
Make the Tzatziki: To a bowl, add the grated cucumber, yogurt, lemon juice and mint and stir to combine. Taste for seasoning and adjust as needed.
Make the Chopped Salad: To a bowl, add the chopped tomatoes and cucumber, fresh herbs, lemon juice, olive oil and vinegar and stir to combine.
Assemble the Greek Nachos: Scatter the pita chips onto the bottom of a platter, then top with the shredded chicken, dollops of hummus, tzatziki sauce and chopped salad.
Garnish the nachos with crumbled feta cheese, chopped olives and diced red onion.