  We present an analysis of the physical conditions in an extreme molecular
cloud in the Antennae merging galaxies. This cloud has properties consistant
with those required to form a globular cluster. We have obtained ALMA CO and
870$\mu$m observations of the Antennae galaxy system with $\sim 0".5$
resolution. This cloud stands out in the data with a radius of $\lesssim 24$~pc
and mass of $>5\times 10^6$~M$_\odot$. The cloud appears capable of forming a
globular cluster, but the lack of associated thermal radio emission indicates
that star formation has not yet altered the environment. The lack of thermal
radio emission places the cloud in an early stage of evolution, which we expect
to be short-lived ($\lesssim 1$~Myr) and thus rare. Given its mass and kinetic
energy, for the cloud to be confined (as its appearance strongly suggests) it
must be subject to an external pressure of P/$k_B \gtrsim 10^8$~K~cm$^{-3}$ --
10,000 times higher than typical interstellar pressure. This would support
theories that high pressures are required to form globular clusters and may
explain why extreme environments like the Antennae are preferred environments
for generating such objects. Given the cloud temperature of $\sim 25$~K, the
internal pressure must be dominated by non-thermal processes, most likely
turbulence. We expect the molecular cloud to collapse and begin star formation
in $\lesssim 1$~Myr.
