The phrase "The Chicago School" is used to denote a modern movement in economic thought (as opposed to either the Austrian school, or
keynesian economics). The movement was started by Frank H. Knight and Jacob Viner in the 1920's at Chicago University. The characteristics of the early Chicago School of 1920-1950 differ considerably from the later Chicago School. They were highly suspicious of "positivistic" economic
methodology and denounced economic
imperialism, arguing for a confined role for economic
analysis (esp. Knight). They were suspicious of the efficiency claims of
laissez faire economics, arguing for it only on a "non-consequential" basis. For the most part, they did not welcome the Keynesian Revolution in
macroeconomics and denounced the
Monopolistic Competition approach in microeconomic theory. To a good extent, the issues these "alternative"
paradigms purported to solve, they felt could be handled reasonably well within the confines of
Neoclassical theory.
In the 1960s, after a series of changes in philosophy following Knight and Viner's departure, the department began to congeal into a new shape, led by George J. Stigler and Milton Friedman. This is what became the "Second" Chicago School, which is perhaps the more famous one. The Stigler-Friedman period was characterized by faithful adherence to Neoclassical economics and maintained itself dead against the economic concept of market failures, reinforcing the Chicago School stance against imperfect competition and Keynesian economics. In macroeconomics, the most renowned ideals of the Chicago School have been those of Monetarism under the leadership of Milton Friedman, their best-known advocate. For the longest time, Chicago was the only school in America not swept by the Keynesian Revolution. It is now identifies almost exclusively with Laissez Faire economics and Monetarism
This writeup is based partially on http://cepa.newschool.edu/het/schools/chicago.htm and partially on my understanding of the Chicago School of economic thought.