  We study the possibility of having CP asymmetries in the decay Kaon(+/-) ->
pion(-/+) lepton(+/-) lepton(+/-) (lepton = muon or electron). This decay
violates Lepton Number by two units and occurs only if there are Majorana
particles that mediate the transition. Even though the absolute rate is highly
suppressed by current bounds, we search for Majorana neutrino scenarios where
the CP asymmetry arising from the lepton sector could be sizeable. This is
indeed the case if there are two or more Majorana neutrinos with similar masses
in the range around 10^2 MeV. In particular, the asymmetry is potentially near
unity if two neutrinos are nearly degenerate, in the sense that the mass
difference is similar to the decay rate. The full decay, however, may be
difficult to detect not only because of the suppression caused by the
heavy-to-light lepton mixing, but also because of the long lifetime of the
heavy neutrino, which would induce large space separation between the two
vertices where the charge leptons are produced. This particular problem should
be less serious in heavier meson decays, as they involve heavier neutrinos with
shorter lifetimes.
