If you are using MacOS, from the Troubleshooting guide:
Jekyll & Mac OS X 10.11Permalink
With the introduction of System Integrity Protection, several directories that were previously writable are now considered system locations and are no longer available. Given these changes, there are a couple of simple ways to get up and running. One option is to change the location where the gem will be installed (again, using sudo only if necessary):
$ gem install -n /usr/local/bin jekyll