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(1-8) because of its atomic thickness(9), high mechanical strength(10), relative inertness and impermeability to all standard gases(11-14). 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(15,16) 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, CO2, Ar, N-2, CH4 and SF6) 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 angstrom-sized pores.