Recent theoretical predictions of ferroelectricity in two-dimensional (2D) van der Waals materials reveal exciting possibilities for their use in scalable low-power electronic devices with polarization-dependent functionalities. These prospects have been further invigorated by the experimental evidence of the polarization response in some of transition metal chalcogenides (TMCs) - a group of narrow-band semiconductors and semimetals with a wealth of application potential. Among the TMCs, molybdenum disulphide (MoS2) is known as one of the most promising and robust 2D electronic materials. However, in spite of theoretical predictions, no ferroelectricity has been experimentally detected in MoS2, while emergence of this property could enhance its potential for electronics applications. Here, we report the experimental observation of a stable room-temperature out-of-plane polarization ordering in 2D MoS2 layers, where polarization switching is realized by mechanical pressure induced by a tip of a scanning probe microscope. We have found an unambiguous evidence of a stable antipolar structure consisting of the monolayers with randomly alternating polarization orientation, which form stable but switchable “antipolar” head-to-head or tail-to-tail dipole configurations. The oppositely polarized layers exhibit different piezoelectric activity, second harmonic generation signal, surface potential and conductivity. Ferroelectric MoS2 belongs to the distorted trigonal structural 1T” phase, where a spontaneous polarization is inferred by its P3m1 space-group symmetry and corroborated by theoretical modeling. The coexistence of switchable polarization and metallic conduction makes 1T”-MoS2 a member of a handful of materials with this unique property. Overall, the experimental demonstration of ferroelectricity in 2D molybdenum disulphide opens new perspectives for the fundamental studies of this compound and enables new functionality, which could be exploited in novel electronic applications.