Preheat oven to 400°F. Line a sheet pan with parchment.
Grate zucchini on the large holes of a box grater. Toss with a pinch of salt and let sit 5–10 minutes. Wrap in a clean towel and squeeze out as much liquid as possible.
In a large bowl, whisk egg, garlic, oregano, celery seeds, salt, and pepper. Add ground chicken and dried zucchini. Mix gently with a fork or hands just until evenly combined. If the mixture feels too wet, fold in optional binder 1 tablespoon at a time.
Use a 1½-tbsp cookie scoop to portion and roll into balls; place on the pan, spaced slightly apart.
Lightly brush or spray the meatballs with oil. Bake 14–18 minutes, or until the centers reach 165°F. Rest 3 minutes before serving.