  Elucidating the nature of the magnetism of a high-temperature superconductor
is crucial for establishing its pairing mechanism. The parent compounds of the
cuprate and iron-pnictide superconductors exhibit N\'eel and stripe magnetic
order, respectively. However, FeSe, the structurally simplest iron-based
superconductor, shows nematic order (Ts = 90 K), but not magnetic order in the
parent phase, and its magnetic ground state is intensely debated. Here, we
report inelastic neutron-scattering experiments that reveal both stripe and
N\'eel spin fluctuations over a wide energy range at 110 K. On entering the
nematic phase, a substantial amount of spectral weight is transferred from the
N\'eel to the stripe spin fluctuations. Moreover, the total fluctuating
magnetic moment of FeSe is ~ 60% larger than that in the iron pnictide
BaFe2As2. Our results suggest that FeSe is a novel S = 1 nematic
quantum-disordered paramagnet interpolating between the N\'eel and stripe
magnetic instabilities.
