In a large bowl, combine the ground chicken, breadcrumbs, egg, minced garlic, chopped red onion, parsley, dill, lemon zest, salt, and pepper. Mix until just combined.
Form the mixture into 1.5-inch meatballs and place them on a parchment-lined baking sheet.
Drizzle olive oil over the meatballs and bake at 400°F (200°C) for about 18–20 minutes until golden brown and cooked through.
Mix together Greek yogurt, grated cucumber, minced garlic, lemon juice, olive oil, chopped dill, and a pinch of salt in a bowl. Chill until ready to serve.
Serve the meatballs warm alongside the tzatziki sauce.