Combine ground chicken, egg, breadcrumbs, crumbled feta cheese, fresh parsley, dried oregano, minced garlic, lemon zest, salt, and black pepper in a large mixing bowl. Mix until just combined and shape into 16-20 small meatballs, approximately 1½ inches in diameter.

Heat olive oil in a large skillet or wide saucepan over medium-high heat. Add the meatballs, leaving space between each one. Cook for 8-10 minutes, turning occasionally until golden brown. Remove the meatballs from the pan and set aside.

In the same pan, add minced garlic and cook for 30 seconds. Add orzo pasta and stir for 1-2 minutes. Pour in chicken broth and bring to a boil. Reduce heat to medium-low, cover, and simmer for 10-12 minutes, stirring occasionally.

Once orzo is tender, stir in butter, lemon juice, and lemon zest. Season with salt and pepper to taste. Gently nestle cooked meatballs back into the pan, cover, and warm through for 2-3 minutes. Remove from heat and garnish with fresh dill, additional feta cheese, and fresh parsley if desired.