Alright, so there seems to be enthusiasm for this. The next step is figuring out the practical details.

How do we create a group study room? The first things that come to mind are a Skype group chat, Google hangouts, and the newly developed browser-to-browser video chat. The latter seems undersupported to me, although I haven't researched it specifically. Skype group chats require at least 1 person to have a premium account, and I'm not sure if you can make a permanent "room".

That leaves Google hangouts. Some searching shows that it used to be possible to make a permanent hangout link, but this function was removed. On that same page, Dori, Google Community Manager, offers a workaround. If you create an event years in the future, the hangout link won't change.

To create a lasting link, go to https://plus.google.com/events and look down at Schedule your next hangout. The Hangout link in the created event (under the date/time) is persistent.

This seems like a reasonable solution. Are there any other video group chat options, beside the 3 I mentioned?
Edit: tsakinis has a fourth option, and immediately put it to use: Tinychat.

Should we have a schedule or planning facility, to bridge the time until we get 85 members?
Edit: Shannon suggests that this thread can be used for discussing strategies and experiments.