Preheat the oven to 425°F(220°C) and line a baking sheet with parchment paper.
Place the grated cucumber in a clean kitchen towel or paper towels and squeeze out excess moisture.
In a bowl, combine all of the sauce ingredients. Mix well. Cover and refrigerate for at least 30 minutes to allow flavors to meld.
In a large mixing bowl, combine ground chicken, egg, breadcrumbs, feta, onion, garlic, parsley, oregano, cumin, salt, and pepper. Mix gently until just combined. Avoid overmixing to keep meatballs tender.
Shape the mixture into small meatballs, about 1 to 1.5 inches in diameter. You should get around 20 meatballs.
Bake them for 15 minutes. Remove and drain on paper towels.
In a large bowl, combine tomatoes, cucumber, bell pepper, onion, olives, and feta.
In a small bowl, whisk together olive oil, red wine vinegar, oregano, salt, and pepper. Pour over the salad and toss gently to combine.
Arrange the chicken meatballs on a serving platter. Serve with a bowl of tzatziki sauce for dipping and the fresh Greek salad on the side.