The Kukulkan Brood was formed as an assault Brood for the Swarm. Initially it remained on Char to protect the Hive Cluster.
The Brood was dispatched to secure the xel'naga artifact on Bhekar Ro. The zerg successfully made planetfall and began infesting the area around the artifact and the local terran colony of Free Haven. An assault on the colony was thwarted by the intervention of Alpha Squadron. By that time the Brood's attention was focused on removing the protoss presence from the artifact. Ultimately the Brood was unable to secure the artifact. Following a terran nuclear strike the energy creature that emerged absorbed all of the protoss and zerg on and near the planet. The Brood was effectively destroyed.
Kukulkan was a feathered serpent god in Mayan mythology.
Notably, the brood was the most short-lived one to be in service of the Swarm given that it did not even last one year.