Monolayers of graphene and hexagonal boron nitride (hBN) are highly permeable to thermal protons. For thicker two-dimensional (2D) materials, proton conductivity diminishes exponentially, so that, for example, monolayer MoS that is just three atoms thick is completely impermeable to protons. This seemed to suggest that only one-atom-thick crystals could be used as proton-conducting membranes. Here, we show that few-layer micas that are rather thick on the atomic scale become excellent proton conductors if native cations are ion-exchanged for protons. Their areal conductivity exceeds that of graphene and hBN by one to two orders of magnitude. Importantly, ion-exchanged 2D micas exhibit this high conductivity inside the infamous gap for proton-conducting materials, which extends from ∼100 °C to 500 °C. Areal conductivity of proton-exchanged monolayer micas can reach above 100 S cm at 500 °C, well above the current requirements for the industry roadmap. We attribute the fast proton permeation to ~5-Å-wide tubular channels that perforate micas' crystal structure, which, after ion exchange, contain only hydroxyl groups inside. Our work indicates that there could be other 2D crystals with similar nanometre-scale channels, which could help close the materials gap in proton-conducting applications.