Linear conducting polymers show ballistic transport, imposed by mobile carriers moving along the polymer chains^1,2, whereas conductance in the extended dimension, that is, between polymer strands or layers, remains weak due to the lack of intermolecular ordering and electronic coupling^{3, 4–5}. Here we report a multilayer-stacked two-dimensional polyaniline (2DPANI) crystal, which shows metallic out-of-plane charge transport with high electrical conductivity. The material comprises columnar π arrays with an interlayer distance of 3.59 Å and periodic rhombohedral lattices formed by interwoven polyaniline chains. Electron spin resonance spectroscopy reveals significant electron delocalization in the 2DPANI lattices. First-principles calculations indicate the in-plane 2D conjugation and strong interlayer electronic coupling in 2DPANI facilitated by the Cl-bridged layer stacking. To assess the local optical conductivity, we used terahertz and infrared nanospectroscopy to unravel a Drude-type conductivity with an infrared plasma frequency and an extrapolated local d.c. conductivity of around 200 S cm⁻¹. Conductive scanning probe microscopy showed an unusually high out-of-plane conductivity of roughly 15 S cm⁻¹. Transport measurements through vertical and lateral micro-devices revealed comparable high out-of-plane (roughly 7 S cm⁻¹) and in-plane conductivity (roughly 16 S cm⁻¹). The vertical micro-devices further showed increasing conductivity with decreasing temperature, demonstrating unique out-of-plane metallic transport behaviour. By using this multilayer-stacked 2D conducting polymer design, we predict the achievement of strong electronic coupling beyond in-plane interactions, potentially reaching three-dimensional metallic conductivity^6,7.