I had exactly the same problem. Fresh install of Ubuntu 18.04 ("Bionic Beaver") today (May 27, 2018) - full fresh install wiping all files on single partition of my laptop hard drive, hence no chance of old settings hanging around. No problems with sound in any other instances.
The answer was this old fix:
No sound from Chrome, sound works fine in Firefox etc (13.10)
Install pavucontrol from the Terminal:
sudo apt-get install pavucontrol
To open pavucontrol from the Terminal:
Select the "Playback" menu and make sure that you have it set to Show Applications. Now, start playing something from Google Chrome. It will show up there, and it will show what output device is being used for Google Chrome. Make sure it is set to the output device you are trying to use.
Just posting here to let everyone else know. Ubuntu and Chromium should know too, since the solution is more than 4 years old :)
Thank you to everyone who posts their solutions here - you ladies and gents have helped me immensely with simple fixes many, many times. Thank you!