You have mail?

Recently, when opening new Terminal sessions in Mac OS X, I've started seeing a familiar old message before the first shell prompt.

Last login: Wed Apr 28 06:27:11 on ttys006
You have mail.
mymac:~ my_username$ 

I assumed some system utility had delivered a notification via /usr/bin/mail. What did the message say?

$ mail
mail: /var/mail/my_username: Is a directory

Indeed, /bin/ls showed an empty my_username directory in /var/mail.

Weird.

In any case I deleted /var/mail/my_username/, and the notifications no longer appear in new Terminal sessions.