We observe the build up of strong (∼50%) spontaneous vector polarisation in emission from a GaN-based polariton laser excited by short optical pulses at room temperature. The Stokes vector of emitted light changes its orientation randomly from one excitation pulse to another, so that the timeintegrated polarisation remains zero. This behaviour is completely different to any previous laser. We interpret this observation in terms of the spontaneous symmetry breaking in a Bose-Einstein condensate of exciton-polaritons.PACS numbers: 71.36.+c, 03.75.Kk, Polariton lasers are coherent light sources based on emission of light from a coherent ensemble of excitonpolaritons -the mixed light-exciton quasiparticles in semiconductor microcavities. The concept of polariton lasing was first proposed in 1996 [1], followed a few years later by reports of coherent polariton emission in microcavities [2,3,4]. Recently, we reported polariton lasing at room temperature in GaN-based microcavities [5]. Apart from being very promising for applications, the concept of polariton lasing involves several fundamental physics issues. Contrary to conventional lasers, polariton lasers emit coherent and monochromatic light spontaneously. This is achieved when mixed light-matter quasiparticles (exciton-polaritons), Bosecondense inside a semiconductor microcavity. BoseEinstein condensation (BEC) of the polaritons is a subject of intense experimental and theoretical research at present. Several experimental works claiming polariton BEC have appeared recently [6,7,8]. Though polariton BEC implies polariton lasing these two phenomena are not identical. For polariton lasing a macroscopically populated quantum state of exciton polaritons must be created, which can be considered as a polariton condensate. Polariton lasing does not require thermal equilibrium in the system or the spontaneous build-up of the order parameter, which are the main criteria for BEC when understood as a thermodynamic phase transition. Which experimental measurement should be considered as decisive proof for the exciton-polariton BEC is still a subject of debate within the community. Thermalisation of the exciton-polaritons detected by angle-resolved photoluminescence (PL) measurements has been considered one of the key criteria for a long time [6,7]. However, a similar angular dependence of the PL has also been observed in GaAs-based photon lasers [9]. The spatial coherence of polariton emission demonstrated in Ref.[6] is characteristic for conventional lasers as well. Recent theoretical work suggests that observation of the spontaneous buildup of the vector polarisation in emission from polariton lasers would be evidence for the spontaneous symmetry breaking in the system [10,11,12]. In turn, spontaneous symmetry breaking is considered to be a smoking gun for BEC ever since the pioneering work of Goldstone [13,14].Here we report observations of the build up of the spontaneous vector polarization at room temperature in bulk GaN microcavities. Unlike the recent low temperature e...