Outpost 3 was an outpost constructed on an asteroid by Starfleet in 2160. This outpost was one of eight Earth Outpost Stations located in Sector Z-6 along the Federation side of the Romulan Neutral Zone. This zone was a strip of space that acted as a buffer between the Federation and the Romulans in the Alpha Quadrant.
In 2266, the Federation lost contact with the base. It was determined by the USS Enterprise that the station was destroyed by an unknown vessel that was later discovered to be a Romulan Bird-of-Prey. (TOS: "Balance of Terror", display graphic)
According to the Star Trek: Star Charts (pg. 66), there were 23 Earth outposts. Outposts 1 to 8 were mentioned in dialog or were seen on the Z-6 Sector map in "Balance of Terror" and Outpost 23 was mentioned in dialog in "Future Imperfect". Outpost 3 was constructed in an area of space that been contested over during the Romulan War Theater of Operations (2156-2160).