The Matrix Element Method (MEM) has proven beneficial to make maximal use of the information available in experimental data. However, so far it has been formulated only in Born approximation. In this talk we discuss the extension to NLO accuracy. As a prerequisite we present an efficient method to calculate event weights for jet events at NLO accuracy. As illustration and proof of concept we apply the method to the measurement of the top-quark mass in e+e- annihilation. We observe significant differences when moving from LO to NLO which may be relevant for the interpretation of top-quark mass measurements at hadron colliders relying on the MEM.