Modern physicists currently say no, but an experiment at the CERN particle accelerator has thrown doubt on Einstein’s theory:
Has a Speeding Neutrino Really Overturned Einstein?
Michio Kaku @ the Wall Street Journal
Physicists fired a beam of neutrinos (exotic, ghost-like particles that can penetrate even the densest of materials) from Switzerland to Italy, over a distance of 454 miles. Much to their amazement, after analyzing 15,000 neutrinos, they found that they traveled faster than the speed of light—one 60-billionth of a second faster, to be precise. In a billionth of a second, a beam of light travels about one foot. So a difference of 60 feet was quite astonishing.
It’ll be interesting to see whether other groups will be able to replicate these results.