  We report the discovery of a threshold in the HI column density of Galactic
gas clouds below which the formation of the cold phase of HI is inhibited. This
threshold is at $N_{HI} = 2 \times 10^{20}$ per cm$^{2}$; sightlines with lower
HI column densities have high spin temperatures (median $T_s \sim 1800$ K),
indicating low fractions of the cold neutral medium (CNM), while sightlines
with $N_{HI} \ge 2 \times 10^{20}$ per cm$^{2}$ have low spin temperatures
(median $T_s \sim 240$ K), implying high CNM fractions. The threshold for CNM
formation is likely to arise due to inefficient self-shielding against
ultraviolet photons at lower HI column densities. The threshold is similar to
the defining column density of a damped Lyman-$\alpha$ absorber; this indicates
a physical difference between damped and sub-damped Lyman-$\alpha$ systems,
with the latter class of absorbers containing predominantly warm gas.
