For some odd reason, Google and others stopped auto-generating armhf binaries of Chromium last year. Version 37 was the last one I could find. Luckily the Ubuntu guys have been building it all along and their version 45 installs really easily on the all-new Debian/Raspbian Jessie on your Raspberry Pi 2.
This was a surprise as this kind of thing usually degenerates into dependency hell.
Here you go (updatred to mention libgcrypt):
wget http://ftp.us.debian.org/debian/pool/main/libg/libgcrypt11/libgcrypt11_1.5.0-5+deb7u3_armhf.deb wget http://launchpadlibrarian.net/218525709/chromium-browser_45.0.2454.85-0ubuntu0.14.04.1.1097_armhf.deb wget http://launchpadlibrarian.net/218525711/chromium-codecs-ffmpeg-extra_45.0.2454.85-0ubuntu0.14.04.1.1097_armhf.deb sudo dpkg -i libgcrypt11_1.5.0-5+deb7u3_armhf.deb sudo dpkg -i chromium-codecs-ffmpeg-extra_45.0.2454.85-0ubuntu0.14.04.1.1097_armhf.deb sudo dpkg -i chromium-browser_45.0.2454.85-0ubuntu0.14.04.1.1097_armhf.deb
It even appears correctly in your desktop menus!
Note: Some users reporting issues in comments that I’m not seeing.
Apart from security fixes and the latest Chromium features, you also get full access to most of the Apps and Extensions in the Chrome Web Store. This includes the Espruino Chrome App, which means you or your kids now have everything you need to develop and deploy Embedded and IoT projects for under €100. Honestly, that’s revolutionary.