The electronic band structure of the Peierls compound NbSe3 has been explored for its symmetries with microspot synchrotron photoemission. The Fermi level crossings and deviations from one-dimensional behavior are identified. Density-functional calculations of the Fermi surfaces confirm the nesting conditions relevant for the two phase transitions. The instability along the chains with superstructure periodicity q = 0.44 A(-1) induces a backfolding of the electronic bands, and the Fermi level crossings appear suppressed. This broken symmetry is observed in the fluctuation regime at more than twice the critical temperature, where the correlation length is strongly reduced.