Quantum oscillations (QOs) in transport and thermodynamic parameters at high magnetic fields are an unambiguous signature of the Fermi surface, the defining characteristic of a metal. Therefore, recent observations of QOs in insulating SmB$_6$ and YbB$_{12}$, in particular the QOs of the resistivity $rho_{xx}$ in YbB$_{12}$, have been a big surprise, pointing to the formation of a novel state of quantum matter. Despite the large charge gap inferred from the insulating behaviour of $rho_{xx}$, these compounds seemingly host a Fermi surface at high magnetic fields. However, the nature of the ground state in zero field has been little explored. Here we report the use of low-temperature heat-transport measurements to discover gapless, itinerant, charge-neutral excitations in the ground state of YbB$_{12}$. At zero field, despite $rho_{xx}$ being far larger than that of conventional metals, a sizable linear temperature dependent term in the thermal conductivity is clearly resolved in the zero-temperature limit ($kappa_{xx}/T(Trightarrow0)=kappa_{xx}^0/T eq0$). Such a residual $kappa_{xx}^0/T$ term at zero field, which is absent in SmB$_6$, leads to a spectacular violation of the Wiedemann-Franz law: the Lorenz ratio $L=kappa_{xx}rho_{xx}/T$ is $10^{4}$-$10^{5}$ times larger than that expected in conventional metals. These data indicate that YbB$_{12}$ is a charge insulator but a thermal metal, suggesting the presence of itinerant neutral fermions. Remarkably, more insulating crystals with larger activation energies exhibit a larger amplitude of the resistive QOs as well as a larger $kappa_{xx}^0/T$, in stark contrast to conventional metals. Moreover, we find that these fermions couple to magnetic field, despite their charge neutrality. Our findings expose novel gapless and highly itinerant, charge-neutral quasiparticles in this unconventional quantum state.
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