The Collaborative International Dictionary of English v.0.48:

Pillow \Pil"low\, v. t. [imp. & p. p. Pillowed; p. pr. & vb.
   n. Pillowing.]
   To rest or lay upon, or as upon, a pillow; to support; as, to
   pillow the head.
   [1913 Webster]

         Pillows his chin upon an orient wave.    --Milton.
   [1913 Webster]