This is unfortunately a limitation in Chrome.  There is a command line parameter you can add (I forget what it is at the moment, but I'll try to find it), but you would need to use it every time you launch Chrome, and I believe it also affects Aero Peek for the Windows taskbar.

Putting the following:

--enable-aero-peek-tabs

into the arguments field of the ObjectDock shortcut should do it.  You'll need to shut down all instances of Chrome for it to take effect, but worst case, that'll require a reboot.

It looks like they removed that flag, and I can't see what other switch might work.  You can see the full list here:

http://peter.sh/experiments/chromium-command-line-switches/

I'm not sure how else to go about getting those tabs, as Chrome doesn't expose them by default, and Tiles can't see them otherwise.