Gum stick

from The Collaborative International Dictionary of English v.0.48

Gum \Gum\, n. [OE. gome, AS. gama palate; akin Co G. gaumen,
   OHG. goumo, guomo, Icel. g?mr, Sw. gom; cf. Gr. ? to gape.]
   The dense tissues which invest the teeth, and cover the
   adjacent parts of the jaws.
   [1913 Webster]

   {Gum rash} (Med.), strophulus in a teething child; red gum.
      

   {Gum stick}, a smooth hard substance for children to bite
      upon while teething.
      [1913 Webster]