I'm wondering the same thing. I was able to install Chromium using the latest Ubuntu Trusty (which is based on Debian Jessie) armhf packages on my Debian Jessie Armbian build running on a Banana Pi M1. I had to install libgcrypt11, chromium-codecs-ffmpeg-extra, and chromium-browser Ubuntu .deb files. The rest of the dependencies were found from the Debian apt sources.
But the performance is unbearably slow. I figured with 1GB and a dual-core ARMv7 processor, that web browsing would be at least decent and on par with the experience you get with smartphones. It's not even close. Since Armbian is a bare bones installation, is it possible that I'd need to install other packages to improve web browsing performance? I'm even running everything off a speedier SSD drive on the SATA port, rather than off of the SD card. I tried Midori and that consistently freezes after loading virtually any webpage. Thanks for any suggestions.
UPDATE: I'm starting to suspect this has a lot to do with the fact that I'm on the mainline kernel without any GPU acceleration. So all of the X11 rendering is handled by the CPU, which naturally is going to be unbearably slow for any graphics intensive programs, like a web browser. This is just an assumption on my part, so I could be wrong. Sadly it looks like I'll have to back off to the legacy kernel until GPU support is added to the mainline kernel.