Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles has been predicted in certain crystalline solids in which either inversion or time-reversal symmetry is brokencite{WanPRB2011,BurkovPRL2011, WengPRX2015,HuangNatComm2015}. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention cite{XuScience2015, LvPRX2015, YangNatPhys2015}. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons cite{anderson1965symmetry,shi2013ferroelectric,kim2016polar}. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, $chi^{(2)}$, leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic $chi^{(2)}$ in the TMMPs TaAs, TaP, and NbAs. With the fundamental and second harmonic fields oriented parallel to the polar axis, the value of $chi^{(2)}$ is larger by almost one order of magnitude than its value in the archetypal electro-optic materials GaAs cite{bergfeld2003second} and ZnTe cite{wagner1998dispersion}, and in fact larger than reported in any crystal to date.
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