  The imminent start of the Large Hadron Collider, which is expected to produce
$\sim 10^8$ $t\bar{t}$ pairs per year, provides an unprecedented opportunity
for top physics. As the top quark is widely expected to be rather sensitive to
effects of new physics, a detailed study of its properties, including rare
decays, is called for. A possible, experimentally distinctive decay is the case
where a top decays to a light quark and a flavor-violating lepton-antilepton
pair. We use an effective operator analysis to place model-independent bounds
on contributions to the decays $t\to u e^{\pm} \mu^{\mp}$ and $t\to c e^{\pm}
\mu^{\mp}$. We enumerate the dimension-six operators which contribute to these
decays and which are invariant under the Standard Model gauge group. We
separate these operators into two classes, one with operators where the top
quark belongs to an SU(2) doublet and thus can contribute at tree level to
low-energy processes, and one class with operators where the top quark is a
right-handed singlet and can only contribute to low-energy processes via loop
diagrams. We use $B$ and $K$ decays to place limits on the coefficients of some
of these operators, but find that several remain unconstrained and could
potentially make observable contributions to top decay.
