In a large mixing bowl, combine the Greek yogurt, grated cucumber, minced garlic, dill, lemon juice, olive oil, salt, and pepper. Mix well until all ingredients are fully incorporated.
Add the shredded or diced chicken to the yogurt mixture and stir until the chicken is evenly coated.
Gently fold in the cherry tomatoes and red onion until well distributed throughout the salad.
Taste and adjust seasoning with additional salt and pepper if needed.
If desired, serve the chicken salad over a bed of mixed greens or in a wrap.