Membranes act as selective barriers and play an important role in processes such as cellular compartmentalization and industrial-scale chemical and gas purification. The ideal membrane should be as thin as possible to maximize flux, mechanically robust to prevent fracture, and have well-defined pore sizes to increase selectivity. Graphene is an excellent starting point for developing size-selective membranes because of its atomic thickness, high mechanical strength, relative inertness and impermeability to all standard gases. However, pores that can exclude larger molecules but allow smaller molecules to pass through would have to be introduced into the material. Here, we show that ultraviolet-induced oxidative etching can create pores in micrometre-sized graphene membranes, and the resulting membranes can be used as molecular sieves. A pressurized blister test and mechanical resonance are used to measure the transport of a range of gases (H(2), CO(2), Ar, N(2), CH(4) and SF(6)) through the pores. The experimentally measured leak rate, separation factors and Raman spectrum agree well with models based on effusion through a small number of ångstrom-sized pores.