A chronometer is a device used to track the passage of time.
Starships use chronometers to keep records of time passing, this can often be useful when something happens to the crew of a ship that causes them to lose track of time. When the USS Enterprise was attacked by the Ngultor, consulting the chronometer informed the crew they had been incapacitated for forty-nine minutes. (EV comic: "Flesh of My Flesh")
Chronometers of Constitution class starships in the 23rd century featured a bridge readout which displayed the time as a stardate and on a shipboard twenty-four hour clock. (TOS episode: "The Naked Time")
Data had an internal chronometer. While experimenting with non-androids' experiences of passing time, William T. Riker advised Data to turn off his internal chronometer in order to make the simulation more real. (TNG episode: "Timescape")