The normalised transverse emittance is a measure of the quality of an electron beam from a particle accelerator. The brightness, parallelism and focusability are all functions of the emittance. Here we present a high-resolution single shot method of measuring the transverse emittance of a 125 ± 3 MeV electron beam generated from a laser wakefield accelerator (LWFA) using a pepper-pot mask. An average normalised emittance of εrms,x,y = 2.2 ± 0.7, 2.3 ± 0.6 π-mmmrad was measured, which is comparable to that of a conventional linear accelerator. The best measured emittance was εrms,x,=1.1 ± 0.1 π-mm-mrad, corresponding to the resolution limit of our system. The low emittance indicates that this accelerator is suitable for driving a compact free electron laser.