We describe measurements of the parity-violating (P-odd) triton emission asymmetry coefficient in the 6Li(n,alfa)3H reaction with polarised cold neutrons. Experiments were carried out at the Petersburg Nuclear Physics Institute (Gatchina, Russia) and at the Institut Laue-Langevin (Grenoble, France). We employed an ionisation chamber in a configuration allowing us to suppress the left-right asymmetry well below 10^(-8). A test for a false asymmetry due to eventual target impurities (zero test) resulted in the value (0.0+-0.5)x10^(-8). As final result we obtained P-odd effect (-8.6+-2.0)x10^(-8).