The electron's charge distribution can be characterised by its electric dipole moment (EDM), which measures the deviation of its electric interactions from purely spherical. According to the standard model, this EDM is some eleven orders of magnitude below the current experimental limit. However, most extensions to the standard model predict much larger values, potentially accessible to measurement. Hence, the search for the electron EDM is a search for physics beyond the standard model. Moreover, a non-zero EDM breaks time-reversal symmetry which, in many models of particle physics, is equivalent to breaking the symmetry between matter and antimatter, known as CP symmetry. New CP-breaking physics is thought to be needed to explain the existence of a material universe. We have used a supersonic beam of cold YbF molecules to measure the electron EDM, obtaining the result a new upper limit with 90% confidence. Our result, consistent with zero, indicates that the electron is spherical at this improved level of precision. Our measurement, of atto-eV energy shifts in a molecule, probes new physics at the tera-eV energy scale. Many extensions to the standard model, such as the minimal supersymmetric standard model, naturally predict large EDMs and our measurement places significant constraints on the parameters of these theories.