You have to be careful in how you define speed before answering this question: do you mean group velocity or phase velocity? And faster than the local velocity of light or the value in vacuo?

It is indeed possible for a particle to travel at a speed greater than the local phase velocity of light through a medium. This is what brings about Čerenkov radiation, which is that eerie blue glow associated with the core of nuclear reactors.

But it is possible to go faster than the speed of light. As space expands, it pushes the rest of space (and therefore its contents) apart, potentially faster than the speed of light.

Not really scientific but a good quote ;- ) : No matter how fast light travels it finds the darkness has always got there first, and is waiting for it. ~Terry Pratchett

Hence the "probably"'s.