How well do we know marsupial phylogeny? I’m guessing that there probably isn’t one most closest relatve, but some group of marsupials that have a common ancestor, similar to the horseshoe crab not being closely related to anything, but most closely related to some ancestral proto-arachnid.
I’m going to go with this guy, as it appears it belongs to Australidelphia, but never left south america.
Well, thanks, ignorance fought. I wasn’t aware of another New World marsupial. In which case, I asked the wrong question, which should have been:
What Australian animal (or clade) is the closest relative to New World marsupials?
What do you mean by “the opossum”? The closest relative of the Virginia Opossum Didelphis virginiana of North America is the Common Opossum of Central and South America Didelphis marsupialis. There are four other species in the genus, found in South America. There are more than 90 other species in the family Didelphidae. They are considered to be the most primitive (basal) family of surviving marsupials.
Also in South America are the rat or shrew opossums, the Caenolestidae. They are next most basal member of the marsupials.
Interestingly, another species of South America, the monito de monte, belongs to a separate family and appears to be more closely related to Australian marsupials than those of the Americas.
Australian marsupials appear to be descended from ancestors that originally lived in South America, crossing from that continent across Antarctica when those continents were still united.
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Well more ignorance fought. I had assumed that marsupials had crossed from Australia when all those places were connected, instead of vice versa, which basically renders my question meaningless. Thanks!
There are lots of cool opossums in Central and South America. My favorite is the Yapok or Water Opossum., which is highly aquatic. It is the only marsupial in which both sexes have pouches. The pouch opens backwards and has a sphincter to make it watertight to protect the young when the female is diving. The male tucks his genitalia into his to make him more streamlined when he swims. Sort of a built-in Speedo.
There is an early and brief Stephen J. Gould essay in The Panda’s Thumb on the North American/South American faunal exchange, which mostly saw the extinction of a sizeable clade of marsupial predators in the face of a North American placental invasion. It’s called Sticking up for Marsupials to give the flavor of his argument 
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The Virginia opossum is a successful counter-radiation northwards, but recentish research seems to hint that opossums as a group may have actually very anciently originated in North America, spread south, then became extinct in the north after the Americas were separated at the end of the Cretaceous. Then they spread back north again after the isthmus of Panama reconnected the continents.