The velocity dispersions of stars near the Sun are known to increase with stellar age, but age can be difficult to determine so a proxy like the abundance of alpha elements (e.g., Mg) with respect to iron, [alpha/Fe], is used. Here we report an unexpected behavior found in the velocity dispersion of a sample of giant stars from the RAdial Velocity Experiment (RAVE) survey with high quality chemical and kinematical information, in that it decreases strongly for stars with [Mg/Fe] > 0.4 dex (i.e., those that formed in the first Gyr of the Galaxys life). These findings can be explained by perturbations from massive mergers in the early Universe, which have affected more strongly the outer parts of the disc, and the subsequent radial migration of stars with cooler kinematics from the inner disc. Similar reversed trends in velocity dispersion are also found for different metallicity subpopulations. Our results suggest that the Milky Way disc merger history can be recovered by relating the observed chemo-kinematic relations to the properties of past merger events.