The Chaos Emerald of Immortality grants its wearer the ability to live forever. Additionally physical damage inflicted upon the wearer is rendered ineffective.
The Chaos Emerald of Immortality is kept in the Pyramid of Robotnikhotep I located in ancient Mobigypt. The mummy of Robotnikhotep literally wears the Emerald around his neck inside of his coffin. It grants him eternal life, but when he takes it off and gives it to Dr. Robotnik he turns to dust. With the help of a Mummified Hedgehog, Sonic is able to defeat Robotnik and return the Emerald to its rightful wearer.
Later Robotnik returns to the Pyramid and steals the Emerald from Robotnikhotep once again. This, along with the other three emeralds transforms Robotnik into Supreme High Robotnik. However he is soon defeated and the Chaos Emerald of Immortality is returned to Mobigypt.