There is cumulative evidence showing that, for the most massive galaxies, the fraction of disc-like objects compared to those with spheroidal properties increases with redshift. However, this evolution is thus far based on the surface brightness study of these objects. To explore the consistency of this scenario, it is necessary to measure the dynamical status of these galaxies. With this aim, we have obtained seeing-limited near-infrared integral-field spectra in the H-band for 10 massive galaxies (M-* \textgreater=10(11) h(70)(-2)M(circle dot)) at z similar to 1.4 with SINFONI at the VLT. Our sample is selected by their stellar mass and EW[O ii] \textgreater 15 A, to secure their kinematic measurements, but without accounting for any morphological or flux criteria a priori. Through this 3D kinematic spectroscopy analysis, we find that half (i.e. 50 +/- 7 per cent) of our galaxies are compatible with being rotationally supported discs, in agreement with previous morphological expectations. This is a factor of approximately 2 higher than what is observed in the present Universe for objects of the same stellar mass. Strikingly, the majority of our sample of massive galaxies show extended and fairly high rotational velocity maps, implying that massive galaxies acquire rapidly rotational support and hence gravitational equilibrium. Our sample also show evidence for ongoing interactions and mergers. Summarizing, massive galaxies at high-z show a significant diversity and must have continued evolution beyond the fading of stellar populations, to become their present-day counterparts.