galloon

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A narrow band or braid used as trimming and commonly made of lace, metallic thread, or embroidery.

from The Century Dictionary.

• noun 1. Originally, worsted lace, especially a closely woven lace like a narrow ribbon or tape for binding.
• noun In modern use:
• noun A fabric similar to the above, of wool, silk, tinsel, cotton, or a combination of any of these, A kind of gold or silver lace with a continuous even edge on each side, used on uniforms, liveries, etc.

from the GNU version of the Collaborative International Dictionary of English.

• noun A narrow tapelike fabric used for binding hats, shoes, etc., -- sometimes made ornamental.
• noun A similar bordering or binding of rich material, such as gold lace.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun obsolete A braided trimming with bullion thread, used on men's coats in the eighteenth century, on women's apparel in the nineteenth, and on such furnishings as draperies or cushions.