We calculate the dissociation rates of quarkonium ground states by tun
nelling and direct thermal activation to the continuum, For hadronic m
atter at temperatures T less than or equal to 0.2 GeV, neither of thes
e mechanisms leads to a sufficiently large dissociation to explain the
experimentally observed suppression of charmonium. Dissociation by se
quential excitation to excited energy levels, although OZI-forbidden,
requires further analysis.