  In a recent work the authors have presented a general algorithm to extend the
Matrix Element Method (MEM) to the hadronic production of coloured partons
taking into account next-to-leading-order (NLO) corrections in quantum
chromodynamics (QCD). In this article, the general algorithm is applied to the
production of single top quarks at the LHC. In particular, the generation of
unweighted events following the NLO predictions is presented. Treating these
events as the result of a toy experiment we illustrate the first application of
the Matrix Element Method at NLO QCD for hadronic jet production. As a concrete
example, we study the determination of the top-quark mass. We show that the
inclusion of the NLO corrections can lead to sizeable effects compared to the
Matrix Element Method relying on leading-order predictions only and that the
incorporation of the NLO corrections is mandatory to obtain reliable estimates
of the theoretical uncertainties. In addition, we find that measuring the
top-quark mass using the MEM in single top-quark production offers an
interesting alternative to mass measurements in top-quark pair production.
