#If you're on Ubuntu or working with a Linux VM...
SSH into your server as a root or do sudo -i.
Then install necessary software:
apt-get update
apt-get install -y xvfb fluxbox x11vnc dbus libasound2 libqt4-dbus libqt4-network libqtcore4 libqtgui4 libxss1 libpython2.7 libqt4-xml libaudio2 libmng1 fontconfig liblcms1 lib32stdc++6 lib32asound2 ia32-libs libc6-i386 lib32gcc1 nano
apt-get install -y python-gobject-2
apt-get install -y curl git
Normal:
xvfb-run --server-args='-screen 0, 1024x768x16' google-chrome -start-maximized > /dev/null &
Start and open a page:
xvfb-run --server-args='-screen 0, 1024x768x16' google-chrome -start-maximized http://www.example.com > /dev/null &
#If you're on Windows..
Use Desktops from the MS SysInternals package. You can spawn your Chrome process directly from the "hidden" desktop and keep it working there (I have not personally tested this).
#Other options...
You could try spawning Chrome as a child process using something like Node.js and piping the output back to the terminal. See runChrome.js for an example of how to do this (todo: update to latest Express).