The USS Grissom was a Federation starship in service during the late 24th century.
In 2366, the Grissom was assigned near the Sigma Eridani system. The USS Enterprise-D had them stand by in case with supplying them with more hytritium in case the Enterprise ran out. (TNG: "The Most Toys")
In 2375, the Grissom was destroyed at the Battle of Ricktor Prime during the Dominion War, with the loss of all but six officers out of a wartime crew of 1,250. Lieutenant Chu'lak, who was assigned to the Grissom in 2365, was one of the six Grissom survivors. (DS9: "Field of Fire")
Appendices
Background
According to the Star Trek Encyclopedia the Grissom was an Excelsior-class starship with the registry NCC-42857.
The first edition of the Star Trek Encyclopedia listed this starship as an Oberth class ship with registry NCC-59314.
The Grissom was named for Gus Grissom, an American astronaut killed during an accidental spacecraft fire in 1967.
Apocrypha
While not strictly canon, the Grissom was mentioned as playing a central role in the life of Mackenzie Calhoun in Pocket Books' Star Trek: New Frontier series of novels written by Peter David. The story of the ship's disastrous Prime Directive violation and loss of its captain, Norman Kenyon, in 2371, is told in the novel Once Burned. While the studio doesn't usually recognize the events of licensed sources such as novels as canon, this story does not contradict any of the history established in this vessel's filmed mentions.