In 2267, the USS Enterprise encountered a black star enroute to Starbase 9. Escaping its high gravity field threw the ship off course and backwards through time almost three centuries. (TOS: "Tomorrow is Yesterday")
Background
It is unclear whether this designation referred to a neutron star or to a black hole. Both are high mass (and therefore, high gravity) objects that do not emit visible light.
Further evidence, however, suggests that the writer, D.C. Fontana, probably meant a black hole. The concept of collapsed stellar objects that do not emit radiation dates to around 1916 and Karl Schwarzchild, but the term black hole did not enter the vernacular until around 1968 – after this episode was written.