Preheat the oven to 400°F.
In a large mixing bowl, combine ground chicken, 2 minced garlic cloves, chopped parsley, egg, crumbled feta, oregano, salt, pepper, olive oil, and breadcrumbs. Mix thoroughly.
Form the mixture into meatballs using about a heaping tablespoon per meatball. Place on a parchment-lined or oiled sheet pan.
If making ahead, cover and store meatballs in the fridge up to 3 days or freeze after flash-freezing on the sheet pan.
For the tzatziki sauce, in a small bowl, combine Greek yogurt, minced garlic, chopped scallion, lime zest, and lime juice.
Grate the cucumber using a medium grate and squeeze out excess water with a clean towel.
If not serving tzatziki right away, store cucumber separately with paper towel, adding it to yogurt along with salt and pepper just before serving.
Bake the meatballs in the preheated oven for 15 minutes, then flip and bake an additional 10 minutes until browned and cooked through.
If baking from frozen, test a meatball for doneness; bake 3-5 minutes longer if needed.
Stir the grated cucumber into the yogurt mixture, season with salt and pepper, and serve the tzatziki alongside the meatballs.