I was looking at the page source on GMail a minute ago and saw a link tag that gave a URL for an Atom feed. Sure enough, go to

https://mail.google.com/mail/feed/atom

<feed version="0.3">
  <title>Gmail - Inbox for windley</title>
  <tagline>New messages in your Gmail Inbox</tagline>
  <fullcount>1</fullcount>
  <link rel="alternate" 
        href="http://mail.google.com/mail" type="text/html"/>
  <modified>2005-11-21T03:18:30Z</modified>
  <entry>
    <title>testing</title>
    <summary/>
    <link rel="alternate" 
          href="http://mail.google.com/mail" type="text/html"/>
    <modified>2005-11-21T03:18:10Z</modified>
    <issued>2005-11-21T03:18:10Z</issued>
    <id>tag:gmail.google.com,2004:1187557503841339412</id>
    <author>
      <name>Phillip J. Windley</name>
      <email>me@my.org</email>
    </author>
  </entry>
</feed>

It's apparently been there for quite a while. I just never knew about it.