Measurements of the resistance of single crystals of (Per)2Au(mnt)2 have been made at magnetic fields B of up to 45 T, exceeding the Pauli paramagnetic limit of BP ≈ 37 T. The continued presence of non-linear charge-density wave electrodynamics at B ≥ 37 T unambiguously establishes the survival of the charge-density wave state above the Pauli paramagnetic limit, and the likely emergence of an inhomogeneous phase analogous to that anticipated to occur in superconductors.PACS numbers: 71.45. Lr, 71.20.Ps, 71.18.+y Fundamental changes can occur within paired-electron condensates subjected to intense magnetic fields [1, 2,3]. If the state is a spin-singlet (with electron spins opposed), as in charge-density waves (CDWs) [4] and s-and d-wave superconductors [5], the energy of the partially spinpolarized electrons of the uncondensed metal eventually becomes lower than condensate energy above a characteristic field known as the Pauli paramagnetic limit [6,7,8]. Continued survival of the condensate requires the formation of a lower energy spatially-inhomogeneous phase, in which pairing is between spin-polarized quasiparticle states [8,10,11,12,13]. The existence of such a phase in superconductors becomes questionable owing to the field-induced kinetic energy of orbital currents, which often suppresses superconductivity more strongly [14,15]. By contrast, pure CDW systems are free from orbital currents, yet their high condensation energies increase the demand on magnetic field strength required to reach the Pauli paramagnetic limit [4]. (Per) 2 Au(mnt) 2 is a rare example where this limit (≈ 37 T) falls within reach of the highest available quasi-static magnetic fields of 45 T [16,17]. In this paper we use temperatures down to 25 mK (roughly one-thousandth of the energy gap) to show that the CDW state surpasses the Pauli paramagnetic limit, signalling the likely appearance of an inhomogeneous phase.Both superconductivity [5] and CDWs [4] form as a consequence of electron-phonon interactions. Superconductors are ground states in which gauge symmetry is broken (where the variation of the magnetic field is dependent on topology) [5], while CDWs exhibit a periodic charge modulation that breaks translational symmetry [4]. The BCS (Bardeen-Cooper-Schrieffer) formalism that applies to superconductivity [18], also conveniently describes the electronic structure of CDWs, with the gap in the electronic energy spectrum in the zero temperature limit being given by 2∆ 0 = ζk B T c , where T c is the transition temperature. Whereas the ratio ζ = 3.52 in weak-coupling BCS theory, 5 < ζ < 10 in CDWs owing to their strong coupling to the ionic lattice [4]. Upon lowering the temperature through T c , a metal-insulator transition occurs, below which normal carriers must be thermally excited across the gap to conduct. The presence of a magnetic field B lowers T c [8]; simple theory predicts T c → 0 at the Pauli paramagnetic limit defined as, where g is the electron g-factor, s is the electron spin and µ B is the electron Bohr magneton.Ap...