The Collaborative International Dictionary of English v.0.48:

Blab \Blab\ (bl[a^]b), v. t. [imp. & p. p. Blabbed (bl[a^]bd);
   p. pr. & vb. n. Blabbing.] [Cf. OE. blaberen, or Dan.
   blabbre, G. plappern, Gael. blabaran a stammerer; prob. of
   imitative origin. Cf. also Blubber, v.]
   To utter or tell unnecessarily, or in a thoughtless manner;
   to publish (secrets or trifles) without reserve or
   discretion; -- sometimes used with out. --Udall.
   [1913 Webster]

         And yonder a vile physician blabbing
         The case of his patient.                 --Tennyson.
   [1913 Webster]