In a large mixing bowl, combine the ground chicken, egg, breadcrumbs, feta cheese, parsley, oregano, minced garlic, lemon zest, salt, and pepper. Mix until just combined.
Shape the mixture into small meatballs about one inch in diameter and place them on a plate.
Heat olive oil in a large skillet over medium heat. Cook the meatballs in batches for about 5–7 minutes on each side until golden brown and cooked through.
In another pot, bring chicken broth (or water) to a boil. Add in the orzo pasta and cook according to package instructions until al dente. Drain any excess liquid and return it to the pot.
Stir in butter (or olive oil), lemon juice, additional lemon zest, minced garlic, salt, and pepper into the orzo. Mix well.
Serve by placing a scoop of lemon orzo on each plate topped with several meatballs. Garnish with fresh parsley or dill and crumbled feta cheese, and serve with lemon wedges.