The Collaborative International Dictionary of English v.0.48:

Esnecy \Es"ne*cy\, n. [See Eigne.] (Eng. Law)
   A prerogative given to the eldest coparcener to choose first
   after an inheritance is divided. --Mozley & W.
   [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

ESNECY. Eldership. In the English law, this word signifies the right which
the eldest coparcener of lands has to choose one of the parts of the estate
after it has been divided.