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Heavy-fermion metals exhibit a plethora of low-temperature ordering phenomena . Among these are the so-called hidden-order phases that, in contrast to conventional magnetic order, are invisible to standard neutron diffraction experiments. One of the structurally most simple hidden-order compounds, CeB6, has been intensively studied for an elusive phase that was attributed to the antiferroquadrupolar ordering of cerium-4f moments . As the ground state of CeB6 is characterized by a more conventional antiferromagnetic (AFM) order , the low-temperature physics of this system has generally been assumed to be governed solely by AFM interactions between the dipolar and multipolar Ce moments . Here we overturn this established picture by observing an intense ferromagnetic (FM) low-energy collective mode that dominates the magnetic excitation spectrum of CeB6. Inelastic neutron-scattering data reveal that the intensity of this FM excitation significantly exceeds that of conventional spin-wave magnons emanating from the AFM wavevectors, thus placing CeB6 much closer to a FM instability than previously anticipated. This propensity for ferromagnetism may account for much of the unexplained behaviour of CeB6, and should lead to a re-examination of existing theories that have so far largely neglected the role of FM interactions.