Dead drunk

from The Collaborative International Dictionary of English v.0.48

Dead \Dead\ (d[e^]d), adv.
   To a degree resembling death; to the last degree; completely;
   wholly. [Colloq.]
   [1913 Webster]

         I was tired of reading, and dead sleepy. --Dickens.
   [1913 Webster]

   {Dead drunk}, so drunk as to be unconscious.
      [1913 Webster]