In a mixing bowl, add the yogurt, garlic, dill, vinegar or lemon juice and olive oil, stir until combined. Grate the cucumber with a hand grater and mix into yogurt mixture. Allow to sit in the refrigerator for 1 hour.
Preheat the grill over medium-high heat
In a small bowl, mix together the paprika, oregano, garlic, salt, pepper, and olive oil. Add chicken and massage until marinade covers the chicken thorougly. Place on hot grill and cook until no longer pink.
Once cooked, remove chicken from the grill and slice into strips.
Add a drop of olive oil to a frying pan and heat over medium-high heat. Warm each pita bread for 1.5 minutes each side.
Assemble the gyro by layering lettuce, chicken, tzatziki, onion and tomato. Serve