The Argelius sector was a spatial region in the Beta Quadrant. This sector was named after the Argelius system.
In October 2151, the Argelius sector was visited by Enterprise NX-01. When Captain Archer told Sub-Commander T'Pol that a Vulcan ship was scheduled to arrive there in two days and then take her back to her homeworld of Vulcan, T'Pol told him she wouldn't have time to finish her scans of the sector. Consequently, she planned to ask Ensign Mayweather to complete them. (ENT: "Shadows of P'Jem")
This sector of space was unnamed on screen; the name "Argelius sector" came from a line of dialogue in the first draft script of "Shadows of P'Jem" (written while the episode had the working title "Untitled Andorians Return"). In the episode itself, T'Pol instead simply refers to it as "this sector".