As part of a vision quest, Tom Paris told Chakotay that word had just come in from Vegas, Mars and Orion III that the odds were 33:1 that Kid Chaos would outpoint him and 11:1 that he'd be k.o.ed by the fifth round. (VOY: "The Fight")
"The Explored Galaxy"
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Orion was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in this quadrant. This chart, first seen chronologically in Star Trek VI: The Undiscovered Country, was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".
The Orion system was located in the Beta Quadrant. This system, also known as Pi 3 Orionis, was a trinary star system. Primary was a Class F star with a magnitude of +3, which was ten times the brightness of Sol. Secondary and tertiary were Class F stars. In 2120, this was a destination on the final voyage of Zefram Cochrane. In the mid-22nd century, this system was in non-aligned space, and was in proximity of the Vulcan trade routes. In the late 24th century, this system was located in or near Federation space, and this system was a destination on the major space lanes. (pgs. 36, 45, 60)