We study the influence of a possible H dibaryon condensate on the equa
tion of state and the overall properties of neutron stars whose popula
tion otherwise contains nucleons and hyperons. In particular, we are i
nterested in the question of whether neutron stars and their masses ca
n be used to say anything about the existence and properties of the H
dibaryon. We find that the equation of state is softened by the appear
ance of a dibaryon condensate and can result in a mass plateau for neu
tron stars. If the limiting neutron star mass is about that of the Hul
se-Taylor pulsar a condensate of H dibaryons of vacuum mass similar to
2.2 GeV and a moderately attractive potential in the medium could not
be ruled out. On the other hand, if the medium potential were even mo
derately repulsive, the H would not likely exist in neutron stars. If
neutron stars of mass similar to 1.6M. were known to exist, attractive
medium effects for the H could be ruled out.