What is the most important part of the application?
Four parts of the application are critically important: 1) your academic record; 2) letters of recommendation submitted by persons able to describe your achievements and promise; 3) a significant example of your work (B.A. essay, M.A. thesis, research or course paper); and 4) the statement of purpose, which describes the intellectual issues and historical subjects to be explored at the University of Chicago. The Department of History considers the writing sample the most important part of your application. When composing the statement of purpose, it is important to be as specific as possible in describing research interests, including area, period, and topic or approach, and faculty members with whom you might wish to work. Although many graduate students change their focus in the course of their studies, it is helpful to have the clearest possible idea of your interests and any research experience to date.
There is not one single most important part of the application. When reviewing an application, admission decisions are made based on all the materials submitted, i.e. educational background and grades, work experience (if any), GMAT/GRE/MAT scores, letters of recommendation, and the statement of objectives.