I am looking for a fable.  Chinese, I believe, but it may be from any
Oriental country.  This fable is about a dragon (or serpent) that ends
up tying itself in a knot chasing a canary (or other small bird). 
What I really want is a picture of the knotted dragon, but if I can
find the origin of the story, I would have better luck at a library.

No mention of it in "Myths and Legends of China", by E.T.C Werner. 

Most mentions of knotted dragons are Celtic, although Chinese would be my guess.

A Chinese jade pendant in the shape of a knotted dragon:
http://www.metmuseum.org/toah/ho/04/eac/hob_1985.214.99.htm

Oh well.  I spent about 4 hours googling for a number of things before
finally resorting to the experts.  I did have to finally exclude the
word celtic to get more oriental references to any sort of knot.

I have not been able to locate a Chinese fable featuring this theme,
but I have found several images of knotted dragons. For instance, here
is an interesting knotted dragon tattoo:

http://www.tattoo.dk/eriks/fotos_drager2/Knude_Drage.jpg

The story of the constellation Draco involves a Greek myth about a
knotted dragon:

"Early Greek myths tell of a great battle between the young gods and
the older ones who had ruled for so very long. The new gods included
Zeus and his brothers Poseidon and Hades. There were also Hera and
Demeter along with Athena and others. Athena was the Goddess of Arts,
Crafts and War. There were also terrifying figures cast up out of the
volcanic fires that belched out of the bowels of Earth. These
monsters, who represented the universal forces of evil, were known as
the Titans, or the Giants. During the battle, which lasted for ten
long years, one the Titans hurled a fierce dragon at Athena. So great
was her strength and so effective her magic shield that Athena was not
frightened. She caught the dragon and, with one mighty heave, swung
him high into the heavens. Up he soared, twisting and coiling this way
and that until his long body had become tied in knots. He came to rest
in the northern sky and became fixed to that region around which the
northern stars circle. Today we see him forever asleep as the
much-knotted, battered, and twisted Draco."

http://www.coldwater.k12.mi.us/lms/planetarium/myth/draco.html