Some heavy fermion materials show so-called hidden-order phases which are invisible to
many characterization techniques and whose microscopic origin remained controversial for
decades. Among such hidden-order compounds, CeB6 is of model character due to its
simple electronic configuration and crystal structure. Apart from more conventional
antiferromagnetism, it shows an elusive phase at low temperatures, which is commonly
associated with multipolar order. Here we show that this phase roots in a Fermi surface
instability. This conclusion is based on a full 3D tomographic sampling of the electronic
structure by angle-resolved photoemission and comparison with inelastic neutron scattering
data. The hidden order is mediated by itinerant electrons. Our measurements will serve as a
paradigm for the investigation of hidden-order phases in f-electron systems, but also
generally for situations where the itinerant electrons drive orbital or spin order
