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Photons experience mirror asymmetry of macroscopic chiral media, as in circular dichroism and polarization rotation, since left and right handed circular polarizations differently couple with matter handedness. Conversely, free relativistic electrons with vanishing orbital angular momentum have no handedness so the question arises whether they could sense chirality of geometrically symmetric macroscopic samples. In this Letter, we show that matter chirality breaks mirror symmetry of the scattered electrons quantum decoherence, even when the incident electron wave function and the sample shape have a common reflection symmetry plane. This is physically possible since the wave function transverse smearing triggers electron sensitivity to the spatial asymmetry of the electromagnetic interaction with the sample, as results from our non-perturbative analysis of the scattered electron reduced density matrix, in the framework of macroscopic quantum electrodynamics. Furthermore, we prove that mirror asymmetry also shows up in the distribution of the electron lateral momentum, orthogonal to the geometric symmetry plane, whose non-vanishing mean value reveals that the electron experiences a lateral mechanical interaction entirely produced by matter chirality.