Magnesium diboride, MgB2, has a relatively high superconducting transition temperature, placing it between the families of low- and high-temperature (copper oxide based) superconductors. Supercurrent flow in MgB2 is unhindered by grain boundaries, making it potentially attractive for technological applications in the temperature range 20-30 K. But in the bulk material, the critical current density (Jc) drops rapidly with increasing magnetic field strength. The magnitude and field dependence of the critical current are related to the presence of structural defects that can 'pin' the quantized magnetic vortices that permeate the material, and a lack of natural defects in MgB2 may be responsible for the rapid decline of Jc with increasing field strength. Here we show that modest levels of atomic disorder induced by proton irradiation enhance the pinning of vortices, thereby significantly increasing Jc at high field strengths. We anticipate that either chemical doping or mechanical processing should generate similar levels of disorder, and so achieve performance that is technologically attractive in an economically viable way.