The Relativistic Heavy Ion Collider (RHIC), as the world's first and only polarized proton collider, offers a unique environment in which to study the spin structure of the proton. In order to study the proton's transverse spin structure, the PHENIX experiment at RHIC took data with transversely polarized beams in 2001-02 and 2005, and it has plans for further running with transverse polarization in 2006 and beyond. Results from early running as well as prospective measurements for the future will be discussed.EI