Got my Chase letter. It warns about not sending information by email. Nothing about not clicking on links. In fact, it contains the lines:
The security of your information is a critical priority to us and we strive to handle it carefully at all times. Please visit our Security Center at chase.com and click on "Fraud Information" under the "How to Report Fraud." It provides additional information on exercising caution when reading e-mails that appear to be sent by us.
chase.com is a link!
All a phisher needs to do is send this exact email, pointing to a dummy Chase page, and encourage the victim to log in when he reaches it.
Clearly they are either very stupid or really just don't care. I'll go for the latter.