  We consider lepton flavour violating decays of the top quark, mediated by
four-fermion operators. We compile constraints on a complete set of
SU(3)*U(1)-invariant operators, arising from their loop contributions to rare
decays and from HERA's single top search. The bounds on e-mu flavour change are
more restrictive than l-tau; nonetheless the top could decay to a jet $+ e
\bar{\mu}$ with a branching ratio of order $10^{-3}$. We estimate that the
currently available LHC data (20 inverse-fb at 8 TeV) could be sensitive to
$BR(t \to e \bar{\mu}$+ jet) $ \sim 6\times 10^{-5}$, and extrapolate that 100
inverse-fb at 13 TeV could reach a sensitivity of $ \sim 1 \times 10^{-5}$.
