Chicago style is typically used in history and other humanities disciplines. You might also see a reference to "Turabian" style, which is just a simplified version of Chicago.
There are two types of Chicago style:
The author-date style uses parenthetical citations (the citation information is within parentheses beside the quoted or paraphrased information). It tends to be used in the social sciences.
The note-bibliography (NB) style requires the use of footnotes or endnotes (the citation information is either at the foot of the page or at the end of the article and is noted at the end of the quoted or paraphrased text with a number in superscript). It tends to be used in history, the arts, and some other humanities.