The Rashba effect is one of the most striking manifestations of spin-orbit coupling in solids and provides a cornerstone for the burgeoning field of semiconductor spintronics. It is typically assumed to manifest as a momentum-dependent splitting of a single initially spin-degenerate band into two branches with opposite spin polarization. Combining polarization-dependent and resonant angle-resolved photoemission measurements with density functional theory calculations, we show that the two “spin-split†branches of the model giant Rashba system BiTeI additionally develop disparate orbital textures, each of which is coupled to a distinct spin configuration. This necessitates a reinterpretation of spin splitting in Rashba-like systems and opens new possibilities for controlling spin polarization through the orbital sector. 2015 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science.