The Collaborative International Dictionary of English v.0.48:

Whilst \Whilst\, adv. [From Whiles; cf. Amongst.]
   While. [Archaic]
   [1913 Webster]

         Whilst the emperor lay at Antioch.       --Gibbon.
   [1913 Webster]

   The whilst, in the meantime; while. [Archaic.] --Shak.
      [1913 Webster]