Charge transport of topological semimetals has been in the focus of intensive investigations because of their non-trivial band topology. Heat transport of these materials, on the other hand, is largely unexplored and remains elusive. Here we report on an observation of unprecedented, giant magnetic quantum oscillations of thermal conductivity in the prototypical Weyl semimetal TaAs. The oscillations are antiphase with the quantum oscillating electronic density of states of a Weyl pocket, and their amplitudes amount to two orders of magnitude of the estimation based on the Wiedemann-Franz law. Our analyses show that all the conventional heat-transport mechanisms through diffusions of propagating electrons, phonons and electron-hole bipolar excitations, are far inadequate to account for these phenomena. Taking further experimental facts that the parallel field configuration favors much higher magneto-thermal conductivity, we propose that the newly proposed chiral zero sound provides a reasonable explanation to these exotic phenomena. More work focusing on other topological semimetals along the same line is badly called for.Charge and heat conductions define two entangled fundamental transport properties of a conducting solid. Controllable manipulations of both are essential for various functionalities of pertinent materials. For the recently discovered topological semimetals, electrical transport has revealed distinct topologically nontrivial properties, like the chiral anomaly in the longitudinal magneto-resistance (MR) [1][2][3][4]. On the other hand, thermal transport, in particular thermal conductivity, has remained largely unexplored. This is mainly due to the technical difficulties of precise thermal management at low temperatures. In addition, such work has been so far considered 1 uninteresting because the thermal conductivity may be estimated from the electrical conductivity through the Wiedemann-Franz (WF) law.Indeed, for most electrical conductors, the WF law can provide a straightforward and reliable approach to the electronic contribution κ e of the thermal conductivity based on the electrical conductivityσ, κ e /T = σ L 0 , (1) with the Sommerfeld value of Lorenz number L 0 ≡ π 2 /3 (k B /2) 2 = 2.44 x 10 -8 W⋅Ω⋅K -2 . The WF law holds in the case of dominant elastic scattering, e.g., from static defects as realized at sufficiently low temperatures [5]. Within the last few years, it was also found that the charge and heat conductions of the relativistic Dirac/Weyl fermions may deviate from the WF law [6][7][8][9][10][11]. For example, it was shown very recently that hydrodynamic transport by relativistic Weyl fermions in a Weyl semimetal WP 2 can lead to L/L 0 < 1 in the temperature range T < 200 K [10]. On the other hand, for the electron-hole plasma at the charge-neutrality point in graphene, considered to form a strongly coupled Dirac fluid, hydrodynamic transport was found between T = 50 and 80 K to result in a much enhanced Lorenz number L ≈ 22 L 0 [11].