  We measure the temporal pair correlation function $g^{(2)}(\tau)$ of a
trapped gas of bosons above and below the critical temperature for
Bose-Einstein condensation. The measurement is performed {\it in situ} using a
local, time-resolved single-atom sensitive probing technique. Third and fourth
order correlation functions are also extracted. We develop a theoretical model
and compare it with our experimental data, finding good quantitative agreement
and highlighting the role of interactions. Our results promote temporal
correlations as new observables to study the dynamics of ultracold quantum
gases.
