Just because you're on a secure website doesn't mean that you're secure

From American Express Emphasis mine.

As an example of phishing, please note that some of our customers reported receiving the following pop-up screen while logged into our secure site. The pop-up screen is known to be a hoax and contains the following information:

Approximate date of the hoax: 3/29/2006 - present
Title of Pop-Up Box : Security Measures [see below]
Information Requested: Social Security Number, Mother's Maiden Name, Date of Birth

Please note that this fraudulent activity may be the result of a computer virus and is not a part of the American Express website. If you received this pop-up box, your computer may have this virus. The use of both anti-virus software and a firewall to protect your PC are strongly recommended.