I quote from Eyolf Østrem the discoverer of this Medieval cantus when it was initially posted on YouTube:
The original version of a well-known Christmas song. Provenance uncertain, but certain aspects of the melody, such as the end of the versus, point towards an origin not in the main continental tradition, but rather in some of the more peripheral provinces, e.g. in the English sphere or possibly in the Scandinavian countries.
Many thanks to Jeff for introducing me to this remarkable piece of musical history.