Chrome also only updates through the distro's upgrade mechanism on Linux; the automatic updates are only for Windows and Os X. As there noted above the update would need root privileges so Chrome would either have to have an updater with the suid bit set or use something like gksudo. The first of those options seems like a particularly bad idea but there are issues with the second as well. Most modern distros have awesome package management and having an application try to circumvent this by self-updating would probably be undesired behavior for the majority of Linux users anyway.
Once again the commenter referred to updating addons:
“Firefox 5.0 (which will be out not long after 4.0) will have completely transparent addon updating - not even a dialog box.”
Extensions you install using Firefox are kept locally, on Linux in your ~/.mozilla/firefox-{version}/{profile}/extensions/ folder. This is the only part that is intended to be self-updated and there is nothing preventing that.
