  $\Delta L =2$ lepton number violation (LNV) at the TeV scale could provide an
alternative interpretation of positive signal(s) in future neutrinoless double
beta $(0\nu\beta\beta)$ decay experiments. An interesting class of models from
this point of view are those that at low energies give rise to dimension-9
vector operators and a dimension-7 operator, both of whose
$0\nu\beta\beta$-decay rates are "chirally suppressed". We study and compare
the sensitivities of $0\nu\beta\beta$-decay experiments and LHC searches to a
simplified model in this class of TeV-scale LNV that is also $SU(2)_L \times
U(1)_Y$ gauge invariant. The searches for $0\nu\beta\beta$ decay, which are
here diluted by a chiral suppression of the vector operators, are found to be
less constraining than LHC searches whose reach is increased by the assumed
kinematic accessibility of the mediator particles. For the chirally suppressed
dimension-7 operator generated by TeV-scale mediators, in contrast,
$0\nu\beta\beta$-decay searches place strong constraints on the size of the new
Yukawa coupling. Signals of this model at the LHC and $0\nu\beta\beta$-decay
experiments are entirely uncorrelated with the observed neutrinos masses, as
these new sources of LNV give negligible contributions to the latter. We find
the prospects for the high-luminosity LHC and ton-scale $0\nu\beta\beta$-decay
experiments to uncover the chirally-suppressed mechanism with TeV-scale LNV to
be promising. We also comment on the sensitivity of the $0\nu\beta\beta$-decay
lifetime to certain unknown low-energy constants that in the case of
dimension-9 {\it scalar} operators are expected to be large due to
non-perturbative renormalization.
