Chromium web browser
Chromium is the upstream project that Google Chrome browser is based on. Fedora did not include Chromium web browser in the official repository due to problems outlined in
http://ostatic.com/blog/making-projects-easier-to-package-why-chromium-isnt-in-fedora
Tom 'spot' Callaway is working with Google to fix the problems in Chromium. Since Fedora does nowaday allow packages to bundle librariers, it is now possible to package Chromium in Fedora and Tom already created a package review for chromium and its dependencies.
Copr repository
Tom is building Chromium packages using copr, but because of how copr works, he does not currently have full multilib support enabled there. This may cause issues when you try to install Chromium from the Copr. These packages are also unsigned.
If you want to get the full multilib tree with signed packages (notably for libusbx.i686 and libusbx.x86_64), go to https://repos.fedorapeople.org/repos/spot/chromium/ and use that repository instead.
Don't forget to import the gpg key: sudo rpm --import https://repos.fedorapeople.org/repos/spot/chromium/spot.gpg
Google Chrome
Since Chromium is upstream for Google Chrome, all the same issues apply. In addition to that, Fedora does not include Google Chrome because it is a proprietary product and bundles other proprietary software such as Adobe Flash plugin. However, Google does maintain a dnf|yum repository for Fedora at
https://www.google.com/chrome/
The link above also includes downloadable RPMs that you may use to install Chrome.