  We consider QCD tt~Z production at the LHC with Z->\bar\nu\nu and
all-hadronic tt~ decays, i.e. pp -> p_T(miss)bb~+4 jets, as a tool to measure
ttZ couplings. This channel has a significantly larger cross section than those
where the Z boson decays leptonically. However, tt~, bb~+4 jet, tt~j and tt~jj
production give rise to potentially large backgrounds. We show that these
processes can be suppressed to an acceptable level with suitable cuts, and find
that adding the p_T(miss)bb~+4 jet channel to the final states used in previous
ttZ couplings analyses will improve the sensitivity by 10-60%. We also discuss
how the measurement of the ttZ couplings may constrain Little Higgs models.
