The preferred way to do this is to use apt pinning. It allows you to install a single package from testing/unstable, without migrating the whole system to testing/unstable. Caution: this will bring also package dependencies to testing. Pay attention at what are you doing.
A complete guide to pinning is here: http://wiki.debian.org/it/AptPreferences
What you need to do is:
Edit /etc/apt/apt.conf and add the following line (or edit a similar line if present)
APT::Default-Release "stable";
Edit /etc/apt/sources.list and add (replace the mirror with your own). You will have a similar line with stable in place of testing. DO NOT EDIT THAT LINE.
deb ftp://http.us.debian.org/debian testing main contrib non-free
Now edit /etc/apt/preferences, and add
Package: chromium-browser
Pin: release a=testing
Pin-Priority: 900
Run apt-get update
; to check that you haven't switched to testing, try to launch a apt-get upgrade. If you see lots of upgrades (maybe upgrade your system just before starting the procedure), abort: something has gone wrong. You may or may not see chromium in the upgrades: if not, upgrade it with
apt-get install -t testing chromium-browser