We argue that the observed antiproton production in heavy-ion collisions at
CERN-SPS energies can be understood if (contrary to most sequential scatte
ring approaches) the backward direction in the process p (p) over bar <----
> (n) over bar pi (with (n) over bar = 5-6) is consistently accounted for w
ithin a thermal framework. Employing the standard picture of subsequent che
mical and thermal freezeout, which induces an oversaturation of pion number
with associated chemical potentials of mu (pi), similar or equal to 60-80
MeV, enhances the backward reaction substantially. The resulting rates turn
out to be large enough to maintain an antiproton abundance at thermal free
zeout in accordance with the measured (p) over bar /p ratio in Pb(158A GeV)
+ Pb collisions.