  We compute the entanglement entropy of a free massive Dirac field between two
causally disconnected open charts in de Sitter space. We first derive the
Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no
supercurvature mode for the Dirac field. We then give the Bogoliubov
transformation between the Bunch-Davies vacuum and the open chart vacua that
makes the reduced density matrix diagonal. We find that the Dirac field becomes
more entangled than a scalar field as $m^2/H^2$ becomes small, and the
difference is maximal in the massless limit.
