USS Chekov, dead in space, as it appeared on Enterprise-D's viewscreen.
The USS Chekov was a Springfield-class starship that fought the Borg at the Battle of Wolf 359 in 2367. It was destroyed, along with 38 other starships. (TNG: "The Best of Both Worlds, Part II")
Background
The ship's name is an homage to the original series character Pavel Chekov. This starship (named Chekhov, after the Russian writer, in the episode script) was originally to be mentioned by name in dialogue in "The Best of Both Worlds", but the writers ultimately felt that the reference would be too "cute" for such a serious moment, and a reference to the Tolstoy was dubbed in during post-production to replace it.
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The name of this ship are derived from the Star Trek Encyclopedia (1999 edition). Its registry according to the model featured at Ex Astris Scientia is NCC-57302. The Encyclopedia, on the other hand, labels the registry as NCC-53702, which could be a typographical error as it appears to differ from the studio model used for the visual effects of the battlefield. Photographs of this model were part of Michael Okuda's art department slideshow given at conventions throughout the 1990s, and more information about it can be found at Ex Astris Scientia's USS Chekov reconstruction.
Apocrypha
In Peter David's novel Vendetta, an Excelsior-class USS Chekov, commanded by Capt. Morgan Korsmo, fought the Borg with the help of the Enterprise-D.