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.

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