1
general::
Also, scarcer than hen's teeth. Exceptionally rare, as in On a rainy night, taxis are as scarce as hen's teeth. Since hens have no teeth, this term in effect says that something is so scarce as to be nonexistent. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): *scarce as hen’s teeth [and] scarcer than hen’s teeth
Cliché scarce; seldom found. (*Also: as ~.) • I do declare, decent people are as scarce as hen’s teeth in these chaotic times. • Handmade lace is scarcer than hen’s teeth; most lace is made by machine.
McGrawhill's American Idioms And Phrasal Verbs