Doable, but if chromium is minimised, you will still see a window manager/background.
I would recommend using a lightweight window manager, like openbox with an empty menu file ~/.openbox/config/menu.xml, so a user cannot active any programs.
Steps
- Install a window manager
 
- Configure window manager settings (blank config so no other programs can be activated)
 
- Configure auto login at boot
 
- Configure X server to start on login (add 
exec startx to ~/.bash_profile) 
- Add window manager to 
~/.xinitrc 
- Add 
chromium to ~/.xinitrc 
If you need to update the Pi, you can Ctrl+Alt+Backspace to get back to the terminal, su to root, update etc.
Be sure that xorg is configured to allow Ctrl+Alt+Backspace with
 Option "XkbOptions" "terminate:ctrl_alt_bksp"    
in /etc/X11/xorg.conf.d/10-evdev.conf.