  Enhanced positron annihilation on polyatomic molecules is a long-standing and
complex problem. We report the results of calculations of resonant positron
annihilation on methyl halides. A free parameter of our theory is the positron
binding energy. A comparison with energy-resolved annihilation rates measured
for CH$_3$F, CH$_3$Cl, CH$_3$Br [Barnes et al. Phys. Rev. A {\bf 74}, 012706
(2006)] shows good agreement and yields estimates of the binding energies.
