  We present the calculation of the NLO QCD corrections to the electroweak
production of top-antitop pairs at the CERN LHC in the presence of a new
neutral gauge boson. The corrections are implemented in the parton shower Monte
Carlo program POWHEG. Standard Model (SM) and new physics interference effects
are properly taken into account. QED singularities, first appearing at this
order, are consistently subtracted. Numerical results are presented for SM and
$Z'$ total cross sections and distributions in invariant mass, transverse
momentum, azimuthal angle and rapidity of the top-quark pair. The remaining
theoretical uncertainty from scale and PDF variations is estimated, and the
potential of the charge asymmetry to distinguish between new physics models is
investigated for the Sequential SM and a leptophobic topcolor model.
