The relation between crystal symmetries, electron correlations, and electronic structure steers the formation of a large array of unconventional phases of matter, including magneto-electric loop currents and chiral magnetism. Detection of such hidden orders is a major goal in condensed matter physics. However, to date, nonstandard forms of magnetism with chiral electronic ordering have been experimentally elusive. Here, we develop a theory for symmetry-broken chiral ground states and propose a methodology based on circularly polarized spin-selective angular-resolved photoelectron spectroscopy to probe them. We exploit the archetypal quantum material Sr2RuO4 and reveal spectroscopic signatures which, even though subtle, may be reconciled with the formation of spin-orbital chiral currents at the material surface. As we shed light on these chiral regimes, our findings pave the way for a deeper understanding of ordering phenomena and unconventional magnetism.