  The first investigation of tripartite entanglement harvesting in the vicinity
of a black hole is carried out. Working in the context of a static
Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole spacetime we find that it is
possible to harvest tripartite entanglement in regions where harvesting of
bipartite entanglement is known to be impossible due to intense Hawking
radiation. In these situations, it implies that the harvested entanglement is
of the Greenberger-Horne-Zeilinger (GHZ) type.
