  We investigate the tunneling magnetoresistance in magnetic tunnel junctions
(MTJs) comprised of Weyl semimetal contacts. We show that
chirality-magnetization locking leads to a gigantic tunneling magnetoresistance
ratio, an effect that does not rely on spin filtering by the tunnel barrier.
Our results indicate that the conductance in the anti-parallel configuration is
more sensitive to magnetization fluctuations than in MTJs with normal
ferromagnets, and predicts a TMR as large as 10^4 % when realistic
magnetization fluctuations are accounted for. In addition, we show that the
Fermi arc states give rise to a non-monotonic dependence of conductance on the
misalignment angle between the magnetizations of the two contacts.
