In a large mixing bowl, combine ground chicken, gluten-free breadcrumbs, Parmesan cheese, beaten egg, salt, pepper, finely chopped onion, and minced garlic. Mix until evenly combined, then form into golf ball-sized meatballs and place on a baking sheet.

In a large skillet, heat olive oil over medium-high heat. Once shimmering, add meatballs in batches, browning for about 6-8 minutes. Remove and set aside.

In the same skillet, reduce heat and add more olive oil if needed. Sauté diced onion, carrot, and celery for about 4-5 minutes until soft.

Stir in tomato paste and mix with vegetables, then pour in red wine and chicken broth. Bring to a simmer for 15-20 minutes.

Once sauce thickens, return meatballs to the skillet. Cover, reduce heat, and braise for 20-30 minutes.

In a saucepan, bring water or chicken broth to a boil. Slowly whisk in polenta, reduce heat, and simmer for 10-15 minutes. Stir in Parmesan cheese, butter, and salt to taste.

Spoon polenta onto each plate, top with meatballs and sauce, and garnish with fresh parsley.