ABSTRACTWe present gas and stellar kinematics of a high-resolution zoom-in cosmological chemodynamical simulation, which fortuitously captures the formation and evolution of a star-forming barred spiral galaxy, from redshift z ∼ 3 to z ∼ 2 at the peak of the cosmic star formation rate. The galaxy disc grows by accreting gas and substructures from the environment. The spiral pattern becomes fully organized when the gas settles from a thick (with vertical dispersion σv > 50 km s−1) to a thin (σv ∼ 25 km s−1) disc component in less than 1 Gyr. Our simulated disc galaxy also has a central X-shaped bar, the seed of which formed by the assembly of dense gas-rich clumps by z ∼ 3. The star formation activity in the galaxy mainly happens in the bulge and in several clumps along the spiral arms at all redshifts, with the clumps increasing in number and size as the simulation approaches z = 2. We find that stellar populations with decreasing age are concentrated towards lower galactic latitudes, being more supported by rotation, and having also lower velocity dispersion; furthermore, the stellar populations on the thin disc are the youngest and have the highest average metallicities. The pattern of the spiral arms rotates like a solid body with a constant angular velocity as a function of radius, which is much lower than the angular velocity of the stars and gas on the thin disc; moreover, the angular velocity of the spiral arms steadily increases as a function of time, always keeping its radial profile constant. The origin of our spiral arms is also discussed.