I'm not certain why, but the page of three Chicago birth certificates is one of the most popular on my site.
One of the certificates is shown in this posting, for Lillian Apgar, born 2 March 1910 in Chicago with her birth being registered on 3 March 1931. Her sister's birth certificate was a delayed one as well. Her other sisters's birth was never recorded and the younger brother is the only child whose certificate was recorded shortly after the actual birth.
There's an article I posted on my site some time ago analyzing these three certificates and summarizing why I think daughter 3 never had a certificate.
My wife is a descendant of this family and I would love to hear from anyone else researching the family. Of course, she descends from the one who has no birth certificate.