It may be possible but probably not in the way most people think. When an object nears the speed of light its mass also nears infinity. Infinite mass would require infinite energy to accelerate. So, accelerating an object to the speed of light is probably not possible because of the energy required.
However, scientists think that space itself expanded faster than the speed of light just after the big bang. They are doing research on moving a part of space faster than light speed with an object isolated within it.
This way space would move faster than the speed of light but the object would be stationary within that space (but moving with it) and not increase in mass. I hope this makes since :)
If this doesn't work there is always the wormhole theory. But that isn't actually light speed travel either.