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The transmission of a wave through a randomly chosen 'pile of plates' typically decreases exponentially with the number of plates, a phenomenon closely related to Anderson localisation. In apparent contradiction we construct disordered planar permittivity profiles which are complex-valued (i.e. have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way reflectionless for all angles of incidence and exhibit a transmission coefficient of unity. Wedoi:10.1103/physrevlett.118.163201 pmid:28474922 fatcat:mmbfp2pwiren5artglk4ldi664