The Immortals

A highly secretive cabal of mystics, wizards, and other scholars in pursuit of --you guessed it-- immortality. "Organization" is a very general term with the Immortals, as each individual cell or group shares little more than an overarching goal. These sects share information freely, but all go about their studies in different methods; some pursuing the allure of undeath and the occult, while others seek the council of extraplanar beings.
The Immortals maintained three known underground sanctuaries that all members could come and go from freely. Otherwise, members of the Immortals were nomadic or intermingled within other societies.
While there was very little in the way of a formal hierarchy besides initiates vs full members, the founder of the organization, the so-called Grand Undying acted as the de facto leader and guide of the Immortals, though precious few members have ever met him face to face.

Feud With the Night's Song Despite their highly secretive and reclusive nature, the Immortals managed to attract the attention of the Night's Song, who took great concern over this completely unknown and uncontrolled cabal dabbling in the dark arts. Rumors reached them about demonic summonings, rituals of undeath, and communication with Illithid, among other things, and so the Night's Song sought to take the offensive. 
They ambushed and captured a mystic in high standing with the Immortals, Grigor Smit, and using supernatural means, extracted from him information on the Immortal's sanctuaries. They then launched simultaneous raids on each sanctuary, scattering the Immortals within to the winds.
Despite the setbacks and loss of personnel, the Immortals as an organization persevered in their work. Many of them gathered at the hidden sanctuary of the Grand Undying, where rumor had it that he had come into possession of a Tome filled with otherworldly knowledge.