HAN is a 3 letter word that starts with H.

1. \Han\, v. t. [Cf. Sw. h["a]gn hedge, inclosure, Dan. hegn
   hedge, fence. See {Hedge}.]
   To inclose for mowing; to set aside for grass. ``A ground . .
   . hained in.'' --Holland.
   
   

2. \Han\, contr. inf. & plural pres. of {Haven}.
   To have; have. [Obs.] --Piers Plowman.
   
         Him thanken all, and thus they han an end. --Chaucer.