see under bad egg.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
Examples from the Web for rotten egg
Historical Examples of rotten egg
The explosive contact gave forth a blast of sputtering sparks and an offensive, rotten-egg smell.The Spell of the Rockies
Enos A. Mills