Is it possible to orbit a black hole at relativistic speed?

I'm wondering if a space ship could be accelerated close to the speed of light by putting it in orbit around a black hole and accelerate it externally e.g. with a las.... The idea would be to give it a final push out of orbit such that it would go along some intended linear trajectory close to the speed of light. Might it even be possible to taget another black hole that can "catch" the ship in it's orbit?

What say you good people of SMP? 😀