Using a paper towel or clean kitchen towel, squeeze the shredded cucumber to get rid of excess water.
Add the drained cucumber, yogurt, dill, mint, lemon juice, olive oil, garlic, salt, and pepper to a large bowl. Mix until fully incorporated.
Add chicken and red onion and mix until well coated.
Chill for 30 minutes before serving. Great on sandwiches, pita, crackers, or on top of a green salad.