Law school is a time to distinguish yourself, and writing competitions are one way to do that. You can sharpen your research and writing skills on a topic of law you care about, and you can potentially show an employer that you have an interest in a relevant area of law. In addition, should you happen to win, your paper could be published in the journal of the organization that sponsored the competition, and you might be invited to an event and have a unique networking opportunity. And yes, there can be cash awards, sometimes running into thousands of dollars.
There are dozens and dozens of annual writing competitions sponsored by just as many organizations and covering a variety of practice areas. The Financial Aid website is a good place to start. When our office receives information about competitions, we post them on our Symplicity job board, but there are many more than we ever see. A simple Google search yields good results. You also can visit bar association websites, such as the American Bar Association, to find other competitions.
