I did Chicago's MA program in IR, and I agree that it's a great starting point to launch PhD applications from. They're very supportive from the very beginning. Even though the program is only a year, a majority of people made great use of their time there. For example, I left there with more than 3 potential solid LORs. In the end, I decided I wanted at least one from my BA thesis advisor. They also offer great advice on SOPs, resumes, and all aspects of the application.
They also have numerous workshops set up to give you a feel for dissertation writing and critique. They really enjoy when master's students get in on the process. You can't leave Chicago and not know what being an academic is about.