Looking through U of Chicago's site today I noticed they encourage you to do it through their site.
"Applicants who submit their applications electronically via the LSACD on the Web should note that it can take up to fourteen days for the Admissions Office to receive a paper copy of their applications. Their applications will not be deemed received (for purposes of the Early or Regular Decision deadlines) until our Admissions Office has received a paper copy from the Law School Admission Council (LSAC)."
"Online Application: The Law School also provides an online application for its students at https://grad-application.uchicago.edu/
intro/law/intro1.cfm. An online application will be processed faster and is more reliable than a paper application, so we encourage you to use this option. "
Given that it's already the end of September and I haven't even sent in my transcripts or LOR's yet, I'm pretty sure this is the option I'll be going for at least for this school. I guess if you're already on the ball, then 14 days isn't a big deal, but I want complete applications before mid-November and I'm already fairly behind.