You need to have Wine installed first. This is found in the repositories or a
newer version can be found at getdeb.net.. Although the Chromium file is a deb
file it requires the Wine compatibility layer to work.On my system it made a
separate menu entry under Codeweavers.

I have installed it on two computers, both running Ubuntu 8.04 with good
results, although it runs noticeably slower on my eeePC. The installation
yielded an error on one computer and I had to clean up
dpkg as a result. The other one was clean. I can't guarantee it will
work for you. It is still experimental on the Google end, so it may not work
well on all systems.