Squeeze excess moisture from the grated cucumber using a clean tea towel.

In a bowl, mix together the cucumber, Greek yogurt, dill, lemon juice, garlic, salt, and pepper until it's fully combined and creamy.

Toss the shredded chicken into the tzatziki mixture, ensuring each piece is coated.

Gently toss the shredded chicken with the tzatziki sauce until well-coated.

Fold in the diced red onion to the salad mixture.

Stuff the tzatziki chicken salad into warm pita bread, serve it on crackers, or lay it over a fresh bed of lettuce.