DISCLAIMER, im not responsable if it breaks your system, althrough i have tested it on a fully updated linux mint12 install and it worked good after downloading and installing dependacys.
1 go to http://www.google.com/linuxrepositories/
to download the keyring, or run in terminal wget -q -O - https://dl-ssl.google.com/linux/linux_signing_key.pub
| sudo apt-key add -
2 after installing the keyring run the next command to add it to the repository sudo sh -c 'echo "deb http://dl.google.com/linux/chrome/deb/
stable main" >> /etc/apt/sources.list.d/google.list'
3 run sudo apt-get update
to install stable run sudo apt-get install google-chrome-stable
to install beta run apt-get install google-chrome-beta
to install unstable bleeding edge run apt-get install google-chrome-unstable
if you got complains of missing dependacys install them and try again
i did before hand sudo apt-get install libnspr4-0d and sudo apt-get install libcurl3
hope its usefull for you
this is my first post here so i hope im doing this in a manner it is understandable for every one.