  Improving a result of Dyer, Frieze and Greenhill [Journal of Combinatorial
Theory, Series B, 2015], we determine the $q$-colorability threshold in random
$k$-uniform hypergraphs up to an additive error of $\ln 2+\varepsilon_q$, where
$\lim_{q\to\infty}\varepsilon_q=0$. The new lower bound on the threshold
matches the "condensation phase transition" predicted by statistical physics
considerations [Krzakala et al., PNAS 2007].
