This answer is outdated and should no more be followed. See https://raspberrypi.stackexchange.com/a/56231/42933 for—since October 2016—the most appropriate answer.
As already shown in the previous answer, the general idea is to use Chromium builds from Ubuntu. Using their staging repository for Chromium security updates is probably not the only way, but not a bad choice either:
- Always up-to-date.
- Only contains Chromium and doesn't contain any unrelated packages.
To add that PPA to your Raspbian Jessie or Debian Jessie on a Raspberry Pi 2 or 3 (won't work on the Raspberry Pi 1), add the vivid version of https://launchpad.net/~canonical-chromium-builds/+archive/ubuntu/stage to your /etc/apt/sources.list or create a new file at /etc/apt/sources.list.d/chromium-ppa.list with the following lines (source repository commented out as by default on Raspbian):
deb http://ppa.launchpad.net/canonical-chromium-builds/stage/ubuntu vivid main
#deb-src http://ppa.launchpad.net/canonical-chromium-builds/stage/ubuntu vivid main
Ubuntu 15.10 Vivid is the Ubuntu release which is closest to Debian/Raspbian 8 Jessie and hence doesn't need any additional non-Raspbian/-Debian packages to be installed to fulfill dependencies. (Ubuntu 15.04 Vivid itself is no more supported, but Chromium builds are still generated for it for some reason unknown to me. If that stops, you might want to switch to either Ubuntu 14.04 LTS Trusty or Ubuntu 15.10 Wily and install the few additional dependencies from normal Ubuntu repositories.)
To being able to verify the downloaded packages, you need to import the according GnuPG key into APT. By using the full fingerprint as key-id when downloading and importing the key you can be as sure to have the right key as with comparing the fingerprint after downloading:
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys DB69B232436DAC4B50BDC59E4E1B983C5B393194
Please verify the above fingerprint against the one published on https://launchpad.net/~canonical-chromium-builds/+archive/ubuntu/stage to be sure to allow the right key to install packages on your system.
Finally you just need to update the package list and install the chromium-browser package:
sudo apt update
sudo apt install chromium-browser
After that you can already call chromium-browser on the commandline. But to see it also in the menu, etc., you might want to log out and in again or just reboot.
