AT: "nt" The Gilliam was a shuttlecraft attached to the USS Enterprise in 2258.
In that year, upon the mobilization of all Starfleet cadets to respond to a distress call from Vulcan, the Gilliam was used to ferry cadets from Hangar 1 in San Francisco, to the Enterprise, which was docked at Starbase 1. (Star Trek)
Background information
Dr. McCoy and Kirk board the Gilliam, bound for the Enterprise
The Gilliam approaching the Enterprise
The Gilliam originally appeared to be a Moore-type shuttlecraft with its nacelles attached to pylons on the ventral sides of the craft. However, in the reveal shot of the Enterprise it was a military shuttle with its nacelles attached to the dorsal sides of the hull.
This ship was named after the Script Supervisor, Dawn Gilliam. (citation needed • edit)