Former One Nation party leader Pauline Hanson could take the last seat in the New South Wales State Parliament.
The ABC reports Ms Hanson is neck and neck with Labor and the Greens for the seat.
Both Labor and the Greens blame each other for a failure to swap preference votes that would have prevented Ms Hanson from being in the running.
The election on 26 March was won by the Coalition in a landslide victory over Labor. So far, it has 69 seats compared to Labor's 20. The Greens have one.
New premier Barry O'Farrell was sworn-in last week. His cabinet members were named on Sunday and officially sworn-in at Government House in Sydney.