Lithium-rich garnets such as Li7 La3 Zr2 O12 (LLZO) are promising solid electrolytes with potential applications in all–solid-state lithium-ion batteries. The practical use of lithium-garnet electrolytes is currently limited by pervasive lithium-dendrite growth during battery cycling, which leads to short-circuiting and cell failure. One proposed mechanism for dendrite growth is the reduction of lithium ions to lithium metal within the electrolyte. Lithium garnets have been proposed to be susceptible to this growth mechanism due to high electronic conductivities [Han et al. Nature Ener. 4 187, 2019]. The electronic conductivities of LLZO and other lithium-garnet solid electrolytes, however, are not yet well characterised. Here, we present a general scheme for calculating the intrinsic electronic conductivity of a nominally-insulating material under variable synthesis and operating conditions from first principles, and apply this to the prototypical lithium-garnet LLZO. Our model predicts that under typical battery operating conditions, electron and hole carrier-concentrations in bulk LLZO are negligible, irrespective of initial synthesis conditions, and electron and hole mobilities are low (<1 cm2 V−1 s−1 ). These results suggest that the bulk electronic conductivity of LLZO is not sufficiently high to cause bulk lithium-dendrite formation during cell operation. Any non-negligible electronic conductivity in lithium garnets is therefore likely due to extended defects or surface contributions.