A few months ago, along with announcing their first DLC for Don't Starve, Klei Entertainment announced that they were working on a co-op mode. A couple of days ago, they put up the closed beta application form on Don't Starve's website. According to their FAQ, they're already alpha testing Don't Starve Together, and over the course of the closed beta, they'll be adding more and more players to the pool until they progress into an open beta. But they aren't sure how long that'll take.
Klei is looking for as varied a group as possible- from people who have put in over 100 hours to people who have never picked it up. If you don't own Don't Starve and get into the closed beta, you'll get a Multiplayer Only version that will only have two unlockable characters. If you already own the game you'll be able to use all of the characters, you'll just have to unlock them separately in DST.
To me, the most interesting part of the form is the part where it asks you to check off the games you have previously played. Some of them make sense, like Minecraft, DayZ, and even Dark Souls II seems plausible. But it also lists some games completely out of left field, like Euro Truck Simulator 2 and Garry's Mod.