If 
is any nonempty partially
ordered set in which every chain has an upper bound,
then 
has a maximal element. This statement
is equivalent to the axiom of choice.
Renteln and Dundes (2005) give the following (bad) mathematical jokes about Zorn's lemma:
Q: What's sour, yellow, and equivalent to the axiom of choice? A: Zorn's lemon.
Q: What is brown, furry, runs to the sea, and is equivalent to the axiom of choice? A: Zorn's lemming.
