We show on the basis of electronic structure calculations that the uranium 5f magnetic moment in URu2Si2 exhibits a unique Ising behavior, which surprisingly, arises from itinerant electronic states. The origin of the unusual Ising behavior is analyzed as due to the peculiar near-Fermi edge nested electronic structure of URu2Si2 involving its strong spin-orbit interaction. The Ising anisotropy has pertinent implications for theories applicable to explaining the Hidden Order phase in URu2Si2. PACS numbers: 71.28.+d,75.30.Gw The origin of the "Hidden Order" (HO) phase emerging below T 0 = 17.5 K in the uranium-based heavy-fermion compound URu 2 Si 2 has remained a mystery even after more than a quarter century of intensive investigations (see, e.g., Ref.[1] for a recent review). This second-order phase transition appears unmistakably in the thermodynamic and transport properties [2][3][4], yet local solidstate probes such as x rays, neutron scattering, NMR or µSR fail to give a clue for the emerging order parameter. Long-range ordered (dipolar) magnetism has been excluded as a cause for the "hidden order" (HO), but in close proximity to the HO phase a long-range ordered antiferromagnetic phase exists, which is stabilized through only a small pressure of ∼ 0.5 GPa [5].Multifarious theories have been proposed to explain the intriguing appearance of the HO phase, see [1] and [6] for an overview. Since the actinide 5f electrons can, in general, assume localized or itinerant character, correspondingly theories adopting localized 5f behavior have been proposed (e.g., [6][7][8][9][10][11]) as well as competing theories based on the assumption of itinerant 5f behavior (e.g., [12][13][14][15][16][17][18][19][20]). In several of the latter models the existence of a Fermi surface instability is typically connected to appearance of an unconventional density wave [17,18], a spin resonance mode [13] or hybridization wave [14] that triggers formation of a Fermi surface gap. Theories based on localized 5f states often elaborate from a mainly localized 5f 2 configuration possibly with some hybridization with conduction electrons [6,11].Experimental evidence in favor of either localized or itinerant 5f behavior is unquestionably crucial. Recent quantum oscillation measurements [21,22] have drawn attention to a previously unrecognized aspect of the HO quasiparticles in URu 2 Si 2 , namely, their extreme Ising character. From the angular dependence of the de Haasvan Alphen amplitudes [23] a g-factor anisotropy g c /g a , along the c and a crystallographic axes, was estimated to exceed 30, implying that HO emerges out of quasiparticles with giant Ising anisotropy [21,22]. This feature has become salient in the quest for understanding the exotic HO and its concomitant superconductivity [6,24]. The Ising behavior of the near Fermi-energy quasiparticles nicely supports the picture of localized 5f states in URu 2 Si 2 , possibly having a small hybridization with conduction electrons [21,22]. This extreme magnetic anisotropy is a cent...