Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes formation of recently reported splay nematic liquidcrystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation (SHG) imaging, which additionally allowed for determination of the splay modulation period to be of the order of 5 -10 microns, also confirmed by polarized optical microscopy. The observations can be quantitatively described by a Landau-de Gennes type of macroscopic theory. SI A. Material RM734 was synthesized according to Ref.[1] and additionally purified as described in Ref. [2]. As determined by means of differential scanning calorimetry phase transition temperatures have been determined to be: isotropic to nematic TIN= 187.9 °C, nematic to second nematic transition at TNNs = 132.7 °C, and a melting point at Tm = 139.8 °C. We used the Gaussian G09e01 suite of programs [3] to determine the B3LYP/6-31G(d) minimized geometry of RM734 shown in Fig.1. The molecular dipole moment calculated by the B3LYP/6-31G(d) level of DFT is of 11.3748D and oriented almost along the molecular long axis.