There's a chrome extension by Google that provides a supported way to ssh on ChromeOS, from the device. There's limited support for SSH keys built in, and there's also a mosh extension.
(It's pretty easy to enable developer mode in order to allow unsigned code to run, and then Ubuntu/other Linux can run it in a chroot, though education/corporate deployments can/should prohibit that by policy, so isn't relevant to the larger discussion, though it means personal ChromeOS laptops can be quite functional.)
It has a built in terminal called crosh, which might have an SSH client built in (I'm not sure). What most people do is download a chrome extension like Secure Shell[1] that lets you ssh from a tab.
crosh> ssh
The 'ssh' command has been removed. Please install the official SSH extension:
https://chrome.google.com/webstore/detail/pnhechapfaindjhompbnflcldabbghjo
crosh>
There's an ssh client in the chrome store($0, I think it's published by google). It runs as a chrome tab (one tab per connection), which means you do waste some screen space for browser UI that doesn't make sense, but it's workable.
You can (or could, anyway) force it to open in a window (right click the app icon and select "open in window"). This allows you to go really fullscreen and fixes control keys (C-w works again rather than closing the tab).
https://chrome.google.com/webstore/detail/secure-shell/pnhec...
(It's pretty easy to enable developer mode in order to allow unsigned code to run, and then Ubuntu/other Linux can run it in a chroot, though education/corporate deployments can/should prohibit that by policy, so isn't relevant to the larger discussion, though it means personal ChromeOS laptops can be quite functional.)