Cell polarization generally occurs along a single well-defined axis that is frequently determined by environmental cues such as chemoattractant gradients or cell-cell contacts, but polarization can also occur spontaneously in the apparent absence of such cues, through a process called symmetry breaking. In Saccharomyces cerevisiae, cells are born with positional landmarks that mark the poles of the cell and guide subsequent polarization and bud emergence to those sites, but cells lacking such landmarks polarize towards a random cortical site and proliferate normally. The landmarks employ a Ras-family GTPase, Rsr1p, to communicate with the conserved Rho-family GTPase Cdc42p, which is itself polarized and essential for cytoskeletal polarization. We found that yeast Cdc42p was effectively polarized to a single random cortical site even in the combined absence of landmarks, microtubules and microfilaments. Among a panel of Cdc42p effectors and interacting proteins, we found that the scaffold protein Bem1p was uniquely required for this symmetry-breaking behaviour. Moreover, polarization was dependent on GTP hydrolysis by Cdc42p, suggesting that assembly of a polarization site involves cycling of Cdc42p between GTP- and GDP-bound forms, rather than functioning as a simple on/off switch.