Crystal structure imperfections in solids often act as efficient carrier trapping centres, which, when suitably isolated, act as sources of single photon emission. The best known examples of such attractive imperfections are well-width or composition fluctuations in semiconductor heterostructures (resulting in the formation of quantum dots) and coloured centres in wide-bandgap materials such as diamond. In the recently investigated thin films of layered compounds, the crystal imperfections may logically be expected to appear at the edges of commonly investigated few-layer flakes of these materials exfoliated on alien substrates. Here, we report comprehensive optical micro-spectroscopy studies of thin layers of tungsten diselenide (WSe2), a representative semiconducting dichalcogenide with a bandgap in the visible spectral range. At the edges of WSe2 flakes (transferred onto Si/SiO2 substrates) we discover centres that, at low temperatures, give rise to sharp emission lines (100 μeV linewidth). These narrow emission lines reveal the effect of photon antibunching, the unambiguous attribute of single photon emitters. The optical response of these emitters is inherently linked to the two-dimensional properties of the WSe2 monolayer, as they both give rise to luminescence in the same energy range, have nearly identical excitation spectra and have very similar, characteristically large Zeeman effects. With advances in the structural control of edge imperfections, thin films of WSe2 may provide added functionalities that are relevant for the domain of quantum optoelectronics.