  The sensitivity of the LHC experiments to the associated production of dark
matter with a single top is studied in the framework of an extension of the
standard model featuring two Higgs doublets and an additional pseudoscalar
mediator. It is found that the experimental sensitivity is dominated by the
on-shell production of a charged Higgs boson, when this assumes a mass below 1
TeV. Dedicated selections considering one and two lepton final states are
developed to assess the coverage in parameter space for this signature at a
centre-of-mass energy of 14 TeV assuming an integrated luminosity of 300
fb$^{-1}$. For a pseudoscalar mediator with mass 150 GeV and maximally mixed
with the pseudoscalar of the two Higgs doublets, values of $tan\beta$ up to 3
and down to 15 can be excluded at 95% CL, if the $H^{\pm}$ mass is in the range
300 GeV-1 TeV. This novel signature complements the parameter space coverage of
the mono-Higgs, mono-Z and $t{\bar t}$+$E_{\mathrm T}^{\mathrm miss}$
signatures considered in previous publications for this model.
