The Tholian sector was a region of space in the Alpha Quadrant.
In the late 2260s, this sector was unsurveyed. An area within the sector was, according to the Federation, free space. This contrasted strongly with the opinion of the Tholian Assembly, the governing authority of the Tholians, who considered this area as a territorial annex.
In 2268, the starship USS Defiant was sent to this sector on a survey mission. During the course of its survey, the ship became trapped in a spatial interphase.
Three weeks later, the USS Enterprise discovered the Defiant and attempted unsuccessfully to recover the starship. During the failed recovery, Captain James T. Kirk became temporarily trapped in the spatial interphase, and it was only with the aid of Commander Spock and the Enterprise that the captain was freed. (TOS: "The Tholian Web")
A year later, after the soul of Captain Kirk was transferred into the body of Janice Lester, the captain pleaded with Spock for help by pointing out that the commander had risked his life and the ship to free him in this sector. The commander noted that this event had been recorded, and that Janice Lester could have learned of the event. (TOS: "Turnabout Intruder")
This sector's quadrant of origin is inferred based on the position of the government claiming it as seen in the star chart appearing in Star Trek VI: The Undiscovered Country.