The Chicago Manual of Style, often referred to as "Chicago," is the preferred citation format for some social science disciplines and most historical journals. It is important to note that Chicago-style citations come in two varieties, of which you will choose only one for your paper:
Read more about both styles and when you might use them at the Chicago-Style Citation Quick Guide.
For course assignments, always check your syllabus or assignment description to see if the professor has named a specific style you are to use. If you're submitting a manuscript to a journal, be sure to check the journal's information for authors on which style they expect.