Question: Which of Hayek's works had a profound influence on those at the University of Chicago?
Answer: Hayek conducted a number in influential faculty seminars while at the U. of Chicago, and a number of academics worked on research projects sympathetic to some of Hayek's own, such as Aaron Director, who was active in the Chicago School in helping to fund and establish what became the "Law and Society" program in the University of Chicago Law School.
Is the question answered in a satisfactory fashion?
no