Gerald Feinberg postulated in 1967 that particles could move faster than light if their rest mass had an imaginary value. This would allow the mass-energy value of the particle to be a real value like everything else in the universe. He named these particles tachyons from the greek word for "swift".
Back in the real world, the only possible evidence of actual tachyons is the electron neutrino.
Source: Alternate View Column AV-61 in the October-1993 issue of Analog Science Fiction & Fact Magazine, written by John G. Cramer.