In a large skillet, cook the chicken in the oil until no longer pink. Set aside.
In a large saucepan, melt the butter. Cook the onion, celery, carrot and garlic until the onions are transparent.
Mix in the flour and cook for around 3-4 minutes. Pour the chicken broth, half and half and milk over the vegetable mixture and cook until the mixture begins to thicken, around 5 minutes. Reduce heat and stir in the gnocchi and chicken. Mix in the rosemary, salt, pepper and nutmeg. Cook until the gnocchi becomes tender, around 8-10 mintues. Stir in the spinach.