Yes, that is exactly what the Chromium browser project is for. You
can definitely use the Chromium code to develop and market your own
browser. Some examples of browsers based on Chromium include
RockMelt, Flock-Chromium, Iron browser, ChromePlus, and Comodo Dragon.
You can get started by reading the Chromium documentation at
http://dev.chromium.org/Home and then follow the links there to
download and build Chromium yourself for Windows, Mac, or Linux.