Here are some classic answers to that question, courtesy of some famous folk:
Aristotle: To actualize its potential. It is the nature of chickens to cross roads.
Roseanne Barr: Urrrrrp. What chicken?
Ludwig van Beethoven: What? Speak up.
Bodhidharma: If you ask this question, you deny your own chicken-nature.
George Bush: To face a thousand points of headlights.
Julius Caesar: To come, to see, to conquer.
John Calvin: It was predestined.
Bill Clinton: Define "road".
Johnny Cochran: The chicken never crossed the road. Some chicken-hating, genocidal, lying public official moved the road right under the chicken's feet while he was practicing his golf swing and thinking about his family.