To get to the other side, dummy. Any kid will tell you that, but actually there are a million different answers. I've collected some of them here. If you know of one which isn't featured here, mail it to me.
Ludwig Wittgenstein:
The possibility of "crossing" was encoded into the objects "chicken" and "road," and circumstances came into being which caused the actualization of this potential occurrence.
Albert Einstein:
Whether the chicken crossed the road or the road crossed the chicken depends upon your frame of reference.
Newton:
The chicken applied force to its body and accelerated across the road.
Heisenberg:
Any attempt to observe the chicken crossing the road will cause it not to cross the road. Therefore we cannot know when or why the chicken crosses the road.
Feynman:
The chicken's movement across the road was determined by the path integral of its interactions with a cloud of virtual chickens.