We use a very large simulation of the concordance LCDM cosmogony to study the clustering of dark matter haloes. For haloes less massive than about 1e13Msun/h, the amplitude of the two-point correlation function on large scales depends strongly on halo formation time. Haloes that assembled at high redshift are substantially more clustered than those that assembled more recently. The effect is a smooth function of halo formation time and its amplitude increases with decreasing halo mass. At 1e11 Msun/h the ``oldest'' 10% of haloes are more than 5 times more strongly correlated than the ``youngest'' 10%. This unexpected result is incompatible with the standard excursion set theory for structure growth, and it contradicts a fundamental assumption of the halo occupation distribution models often used to study galaxy clustering, namely that the galaxy content of a halo of given mass is statistically independent of its larger scale environment.