  We address the puzzling observational indications for very "cold" galactic
discs at redshifts $z \gtrsim 3$, an epoch when discs are expected to be highly
perturbed. Using a high-resolution cosmological zoom-in simulation, we identify
such a cold disc at $z\sim 3.5$, with a rotation velocity to velocity
dispersion ratio of $v_\phi/\sigma_r \simeq 5$ for the total gas. It forms as a
result of a period of intense accretion of co-planar, co-rotating gas via cold
cosmic-web streams. This thin disc survives for $\sim 5$ orbital periods, after
which it is disrupted by mergers and counter-rotating streams, longer but
consistent with our estimate that a galaxy of this mass
($M_\star\sim10^{10}\mathrm{M_\odot}$) typically survives merger-driven spin
flips for $\sim 2-3$ orbital periods. We find that $v_\phi/\sigma_r$ is highly
sensitive to the tracer used to perform the kinematic analysis. While it is
$v_\phi/\sigma_r \simeq 3.5$ for atomic HI gas, it is $v_\phi/\sigma_r \simeq
8$ for molecular CO and H$_2$. This reflects the confinement of molecular gas
to cold, dense clouds that reside near the disc mid-plane, while the atomic gas
is spread into a turbulent and more extended thicker disc. The proposed
mechanisms is a theoretical proposal that has not been validated yet with
proper statistical measurements and it remains unclear whether it occurs
frequently enough to explain the multiple discoveries of cold gas disks in
high-z galaxies.
