The USS Challenger (NCC-2032) was a Federation starship operating in the 23rd century.
In 2293 the Challenger conducted a deep space exploration mission near Klingon territory. It was among the task force that would have been assembled for the abandoned assault code-named Operation Retrieve, which would have rescued Captain James Kirk and Doctor Leonard McCoy from Qo'noS in 2293. (Star Trek VI: The Undiscovered Country)
Background
The icon representing the Challenger on the barely-visible chart in the Federation President's office was a Template:ShipClass starship, according to Michael Okuda. However, all ships on that chart save the USS Excelsior had the same icon, so it's very unlikely that the Challenger's class can be determined. This ship is not related to the Template:ShipClass of starships, which were employed during the 2360s.
In the non-canon board game Star Fleet Battles, USS Challenger is a Byrd-class Galactic Survey Cruiser, a modification of the Template:ShipClass which replaces the photon torpedoes with special scientific sensor equipment. As a tribute to the space shuttle Challenger, USS Challenger is never to be used in any story or scenario where it could possibly be destroyed.
This starship may have been named after the British corvette HMS Challenger which became the first ship in 1872 to chart the depths of the Earth's oceans. Later ships, including the Apollo Lunar Module Challenger and the space shuttle Challenger, were named in honor of this 19th century ship.