There's a Briton in town seeking to stop at all of the CTA's 144 "L" stops according the CTA Tattler blog. Then I was alerted to an FB group for those who had actually traversed the L system in the shortest amount of time. And according to that page it was roughly three hours.
As of January of this year, I have traversed all of the CTA rail lines. Athough I didn't do it in three hours. I have only done it within the last 12 years.
In 1998 I took the Blue Line all the way to O'Hare. In 1999, I not only took the Red Line from 95th all the way to Howard, but also took the Purple Line to Linden. Also I took the Blue Line to both 54th/Cermak & Forest Park. Also in 1999 I departed from both 63rd/Ashland and 63rd/Cottage Grove on the Green Line to travel downtown.
In 2001, I took the Orange Line all the way to Midway and back to the loop. In 2006 I took the Brown Line all the way to Kimball and also the Green Line to Harlem/Lake. I took the Purple Line express on the way to a temp job in Evanston in early 2008. Also in 2009, I took a ride on the Pink Line to 54/Cermak. Finally in 2011 I took the Yellow Line to Skokie.
If I was to do all that again it wouldn't take me roughly 12 years, but I'm not going to make a world-record time about it either. :P