Measurement of a non-zero electric dipole moment (EDM) of the electron within a few orders of magnitude of the current best limit of |de| < 1.05 × 10-27 e×cm  would be an indication of physics beyond the Standard Model. The ACME Collaboration is searching for an electron EDM by performing a precision measurement of electron spin precession in the metastable H3Δ1 state of thorium monoxide (ThO) using a slow, cryogenic beam. We discuss the current status of the experiment. Based on a data set acquired from 14 hours of running time over a period of 2 days, we have achieved a 1-sigma statistical uncertainty of δde = 1 × 10-28 e×cm/√T, where T is the running time in days. © Owned by the authors, published by EDP Sciences, 2013.