This seems to be a fairly common problem, evidenced by Googling. I have installed Jekyll quite a few times on Windows but this was on a clean install of Ubuntu 16.10...
jack@jakobuntu:~$ gem install jekyll
Fetching: public_suffix-2.0.5.gem (100%)
ERROR: While executing gem ... (Gem::FilePermissionError)
You don't have write permissions for the /var/lib/gems/2.3.0 directory.