A related entry suggests support could come with Chrome OS version 66, which is due out in stable release around April 24, meaning Google might announce it at its annual IO developer conference, which starts on May 8.
There's also a Crouton extension called Xiwi to enable using an OS in a browser window on Chrome OS. However, it too requires developer mode to be enabled.
A recent commit suggests Chrome developers are working on a project called Crostini that may solve the developer mode problem by allowing Linux VMs to run inside a container.
As Chrome Unboxed notes, the commit for Crostini project only refers to developer builds of Chromium, however another commit suggests it could be enabled for all devices.
"If the policy is allowed, the Chrome settings page will include a new menu item entitled 'Better Together Settings'. Fitting, given that Ubuntu runs perfectly alongside Chrome OS," notes Chrome Unboxed.