The basic characteristics of this Chicago Tradition are: a strong work ethic, an unshakable belief in economics as a true science, academic excellence as the sole criterion for advancement, an intense debating culture focused on sharpening the critical mind, and the University of Chicago's two-dimensional isolation. Much of the credit for the creation of this Chicago Tradition has to go to the University's first president, William Rainey Harper.
That is from Johan van Overtveldt's The Chicago School: How the University of Chicago Assembled the Thinkers Who Revolutionized Economics and Business. I enjoyed this book very much. Instead of stopping at Friedman, Coase and Director, it also offers a comprehensive treatment of the entire Chicago history, including such neglected figures as Herbert Davenport, Laurence Laughlin, H. Gregg Lewis, Albert Rees, Theodore Yntema, and Jim Lorie, in each case noting their roles in the broader story.
There is a separate chapter on each the business school and yes the law school. It is also noted that Friedman (among many others) really didn't want Hayek in the economics department. I wish this book had more analysis of how Chicago succeeded in changing the policy world, but it is a landmark in the history of economic thought and of course also law and economics. I can't recommend it to non-specialists, but anyone who cares about Chicago thought should buy it.
A modified version of this post has appeared at www.marginalrevolution.com.