Using ssh keys on a stock Chromebook
Using ssh without passwords from your Chromebook
It is not necessary to switch into developer mode on your Chromebook to use ssh keys.
Ssh keys can be used on a stock Chromebook
The Samsung Chromebook
After several months I am still happy with my Samsung Chromebook. It is absolutely silent, boots very fast and runs very long on the battery. It has a good screen and is very light and thin. It has a good keyboard, great for speedy touch type.
As I use my laptops most of the time just to ssh into Linux boxes and FreeBSD boxes the Chromebook has plenty of functionality for me.
SSH on the Chromebook
You can install the SSH client from the Chromebook app store. After the installation is finished, be sure to set the menu to open the ssh client in its own window.
When you open the SSH client in a new browser tab the browser key bindings get in your way, that is why it is better to let the SSH client run in its own window.
Use Alt-Shift to select the proper keyboard
To prevent all kind of Termcap problems, it is best to choose the US keyboard settings on your Chromebook. If you have a different keyboard you can rotate between the keyboard-settings with Alt-Shift.
Import your ssh keys
Put your private en public ssh key files somewhere where the file manager can find them. This could be on your local download directory, or a SD card or even your Google drive (although I would not do that ...).
Now open the ssh client and click on "Import". You can choose multiple files to import. I did import both the public key as the private key in one go. After this, you can connect password-less to your server.