Orion III

Orion III was a planet located in the space of the galaxy's Beta Quadrant, in the Orion sector of the Sirius sector block.

Details and history
The third planet in orbit of the Orion star system, Orion III supported a population with cordial ties to the Federation. This world was, according to some accounts, a center for gambling. In a vision quest experienced by Chakotay, he imagined being in a boxing match, with book-makers from Las Vegas, Mars and Orion III all agreeing on 33 to 1 odds that Kid Chaos would outpoint Chakotay and 11 to 1 odds that Chakotay would be knocked out by the fifth round. 

Background
establishes the Orion system mentioned in canon as being Pi-3 Orionis, a non-Federation location. extrapolates on the location shown in Star Charts with sector and sector block naming for the vicinity.

Since Star Charts has specific notation regarding Federation and non-Federation worlds, we can see that the political status of this world is not as a Federation member, but it is entrenched in Federation space, and is, apparently, open to exchange sports and betting information with Federation worlds.