In Medieval times, the peasants sometimes could obtain pork, which made them feel quite special. When visitors came over, they would hang up their bacon to show off. It was a sign of wealth that a man ‘could bring home the bacon.’ They would cut off a little to share with guests and would all sit around and “chew the fat.”
It has been pointed out that this is not the right origin for this phrase.
(as stated on Wikipedia: http://en.wikipedia.org/wiki/Chew_the_fat#Email_hoax)