Okay, we all know the proverbial "Chicken Jokes".
Here are some responses you may have never heard before:
Question : Why Did the Chicken Cross the Road?
Select Answers from :
From the U.S.S. Enterprise (A):
Scotty: Because she couldna take much morrrrrre.
Bones: Dammit, I'm a doctor, not an ornithologist!
Uhura: Shall I open hailing frequencies so you can ask it, sir?
Sarek: Sometimes logic fails me where chickens are concerned.
Worf: I don't know. KLINGON chickens do NOT cross roads.
Data: The chicken, in observing that it was on the opposite side of the 20th century Terran paved roadway, was aware that its immediate goal should have been to traverse the distance without interception by an kind of combustion-propelled personal transport vehicle, but I am unclear as to why any kind of domesticated fowl should desire to perambulate upon a conveyance normally reserved for the usage of . . . yes, sir.
Q: Wouldn't you like to know? Too bad your puny human brain wouldn't be able to comprehend the answer.
From the Station
Deep Space 9: 
The Grand Nagus: You Stupid Chicken! You don't cross the road all at once! You sneak across it quietly, without anyone noticing!
Dax: To get to the other side. Kurzon might have disagreed with me...
Gowron: We will defeat the chicken and it will be a glooorious victory for the Klingon Empire.
O'Brien: No problem, Commander, I'll get right on it.
Chakotay: Whatever its reason, whatever its goals, we should respect its right to cross the road and seek its own spiritual awareness.
Neelix: Actually, Captain, I'm not really familiar with the chickens in this system. But, if you can catch it, I can cook it.
HoloDoc: How should I know? No one tells me anything around here. I didn't even know we added chickens to the crew. All I know is that it would have been nice, BEFORE the chicken went off to the cross the road, if it had remembered to turn me off!
Paris: Well, I think that...say, that's a lovely shirt you're wearing.
