Make chicken marinade by combining yogurt, lemon juice, olive oil and spices. If using large chicken breasts, cut into smaller chunks, maybe 3 inches in size. Combine marinade and chicken in a large zip lock bag or other sealable container and make sure all chicken is coated. Place in the fridge for 1+ hours, or overnight (longer is better).
If making Tzatziki: peel, seed and finely chop or shred cucumber; mince garlic cloves, and combine with 1 cup yogurt, red wine vinegar, lemon juice, dill, and salt and pepper in a sealable container and allow to chill in the fridge for 1+ hours.
Once the chicken is done marinating, heat the oven to 425* F and line a large baking sheet with foil. Place chicken evenly spaced on the baking sheet and bake in the oven for 25-30 minutes, removing when the chicken is no longer pink when cut into. Allow to sit for a few minutes, then cut into strips and serve with tzatziki on pitas with tomatoes and red onion, or on a salad.