The First Alpha Centauri Conference was a diplomatic meeting held between Humans, Vulcans and the Andorians.

This conference was the result of the violent first contact between the Andorian Empire and Earth. It was only through the calm and collected actions of the Vulcans was the peace preserved. This was done so when the Vulcans convinced the Andorians that there was nothing to gain and everything to lose if war was to break out.

After the conference, Andor joined the alliance of races that eventually developed into the United Federation of Planets. (FASA RPG module: Star Trek III Sourcebook Update)

Presumably, the conference was held at Alpha Centauri. This information would appear to have been contradicted by the depiction of early Terran-Andorian relations in Star Trek: Enterprise.