Not with any kind of reaction engine anyway. What we have now propels the craft forward by expelling reaction mass backward (equal and opposite). To exceed the speed of light you would need to expel mass at greater than the speed of light. I'm no rocket scientist, but I don't see how we can do that.
Guess we'll have to cheat in some sci-fi fashion, like harnessing wormholes or folding space...
Use particles that have a negative mass.
"Squish just like grape."