The fabrication of crystalline 2D conjugated polymers with well-defined repeating units and in-built porosity presents a significant challenge to synthetic chemists. Yet they present an appealing target because of their desirable physical and electronic properties. Here we report the preparation of a 2D conjugated aromatic polymer synthesized via C-C coupling reactions between tetrabromopolyaromatic monomers. Pre-arranged monomers in the bulk crystal undergo C-C coupling driven by endogenous solid-state polymerization to produce a crystalline polymer, which can be mechanically exfoliated into micrometre-sized lamellar sheets with a thickness of 1 nm. Isothermal gas-sorption measurements of the bulk material reveal a dominant pore size of ~0.6 nm, which indicates uniform open channels from the eclipsed stacking of the sheets. When employed as an organic anode in an ambient-temperature sodium cell, the material allows a fast charge/discharge of sodium ions, with impressive reversible capacity, rate capability and stability metrics.