In 1994, long-serving Country Liberal Party minister Roger Vale announced his resignation as the member for the electorate of Braitling, and Braham decided to nominate in the preselection contest to decide his replacement. She had some difficulty in winning pre-selection, at one point seeking the advice of soon-to-be Chief Minister Shane Stone, but eventually prevailed. As Braitling has usually been a very safe seat for the CLP, Braham was easily elected, and subsequently became the first woman ever to be elected to the Assembly from central Australia.
