In Firefox, while focused on a drop-down box, use ALT-DOWN would display the list so that user can navigate.
But in Chrome, ALT-DOWN does not work, I can only use UP/DOWN to navigate per entry.
I don't believe there's a shortcut to do that. It's not listed in the Chrome Keyboard Shortcuts list and I tried every shortcut I could think of in the latest dev Chrome with no success. I didn't see any issues addressing it in the Chrome issues database so I created one - issue 73349.