I'd heard rumors about this for a while. I presume that the posting of this on the arxiv means that some form of this paper is in submission out there to a suitably glossy, high impact journal that requires reference citations in its abstracts. Background: Bulk FeSe superconducts below around 8 K at ambient pressure (see here). Under pressure, that transition can be squeezed up beyond 35 K (see here). The mechanism for superconductivity in this material is up for debate, as far as I know (please feel free to add a reference or two in the comments).
These investigators have a very fancy ultrahigh vacuum system, in which they are able to grow single layer FeSe on top of SrTiO3 (with the substrate doped with niobium in this case). This material is not stable in air, and apparently doesn't do terribly well even when coated with some protective layer. However, these folks have a multi-probe scanning tunneling microscope system in their chamber, along with a cold stage, so that they can perform electrical measurements in situ without ever exposing their single layer to air. They find that the electrical resistance measured in their four-point-probe configuration drops to zero below around 100 K (as high as 109 K, depending on the sample). One subtle point that clearly worried them: SrTiO3 is know to have a structural phase transition (the onset of ferroelasticity - see here) at around 105 K, so they wanted to be sure that what they saw wasn't somehow an artifact of that substrate effect. (Makes me wonder what happens to superconductivity in the FeSe depending on the ferroelastic domain orientation underneath it.) For the lay audience: liquid nitrogen boils at ambient pressure at 77 K. This would be the first iron-based superconductor to cross that threshold, a domain previously limited to the copper oxides. Remember, if the bulk transition is at 8 K and the single layer case exceeds 100 K, it doesn't seem crazy to hope for some related system with an additional factor of three or four that takes us beyond room temperature.
Important caveats: Right now, they have resistance measurements and tunneling spectroscopy measurements. Because of the need for in situ measurement they don't have Meissner data. It's also important to realize that the restrictions here (not air stable; only happens in single layer material when ultraclean) are not small. At the same time, this is potentially very exciting, and hopefully it holds up well and can be the foundation for more exciting materials.