Make Sauce: Grate cucumber on a cheese grater (or finely mince). Place grated cucumber in cheesecloth and squeeze as much of the liquid from it as possible; set aside.
In a medium mixing bowl, combine yogurt, mayonnaise, garlic, lemon zest, lemon juice, salt and pepper. Add shredded cucumber. Cover and refrigerate.
Make Salad: Place chicken thighs on a small baking sheet lined with aluminum foil. Sprinkle with salt and pepper and bake for 25 to 30 minutes or until done. Remove from heat and let cool.
Remove and discard skin and bones. Shred meat and place in a large bowl. Add feta, onion, eggs, cucumber and dill and mix until incorporated. Add sauce to chicken mixture. Let chill in refrigerator for at least 1 hour to give flavors time to meld. Remove from refrigerator and stir. Check for seasoning and season to taste, if necessary, before serving.
When seasoning with salt, take into account the saltiness of the feta and olives.
The dressing can be made a day ahead of time; cover and refrigerate until use.