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 ^ { \prime \prime } .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 .