We propose a new, sunken continent beneath the North Atlantic Ocean that we name Icelandia. It may comprise blocks of full-thickness continental lithosphere or extended, magma-inflated continental layers that form hybrid continental-oceanic lithosphere. It underlies the Greenland-Iceland-Faroe Ridge and the Jan Mayen microplate complex, covering an area of ~600,000 km². It is contiguous with the Faroe Plateau and known parts of the submarine continental rifted margin offshore Britain. If these are included in a “Greater Icelandia,” the entire area is ~1,000,000 km² in size. The existence of Icelandia needs to be tested. Candidate approaches include magnetotelluric surveying in Iceland; ultralong, full-crust-penetrating reflection profiling along the length of the Greenland-Iceland-Faroe Ridge; dating zircons collected in Iceland; deep drilling; and reappraisal of the geology of Iceland. Some of these methods could be applied to other candidate sunken continents that are common in the oceans.