As many sources mention, users at the website Planet Hunters.ORG have found a planet 5,000 light years away that orbits four Suns. To celebrate the website, it was called PH1.
The observation was made by watching variations in the brightness and it was reported on the arXiv in the decently looking article
However, the four stars are actually ordered hierarchically. Two of the stars are close to each other; and two remaining stars are close to each other, too. So it's really one binary star orbiting another binary star. The planet is very close to one of the pairs.
In this setup, there is nothing too shocking about the stability of the system. The neighborhood of each binary star pretty much ignores the distant binary star system while the planet views the nearby binary star as a single object, when it comes to its trajectory. So the orbits are still essentially Kepler orbits.
I would like to mention that this source of stability is kind of cute and particle physicists who spend lots of time by thinking about the hierarchy problem(s) should think about it, too. Large hierarchies may look unnatural but they actually have an advantage: they help to make systems such as this quadruplet of stars more long-lived.
Can't the hierarchies in particle physics resemble the distances between the stars? And isn't there some explanation of the hierarchies based on this evolutionary advantage? I mean that the Universes with e.g. generic mass ratios of order one have already "destroyed themselves" in some new way. And if there is an explanation of this sort, does it count as an anthropic one?