Starbase 27 was a Federation starbase that was administered by Starfleet. Omicron Ceti III was located near this base.
On stardate 3417, the residents of the Omicron colony were evacuated to this facility by the USS Enterprise on the orders of Admiral Komack. (TOS: "This Side of Paradise")
The unnamed planet seen in TNG: "Ethics" was identified as Starbase 27 in the script of the episode, but this detail was cut from the filmed episode.