Download https://github.com/broberson/coreos-nano/raw/master/nano.tgz and extract to your root directory:
cd /home/core
wget https://github.com/broberson/coreos-nano/raw/master/nano.tgz
cd /
sudo tar zxvf /home/core/nano.tgz
sudo mkdir -p /opt/share/misc
sudo touch /opt/share/misc/magic
This will place nano in your path at /opt/bin. Supplementary files for nano are placed in /opt/etc and /opt/share, where this binary has been configured to expect them.
You should also add the following to the top of your ~/.bashrc file
export MAGIC=/opt/share/misc/magic
If binaries worry you, execute run.sh to build your own copy. If you want to run this on your CoreOS installation directly, change "$(pwd)/:/media/root" to "/:/media/root" in run.sh and delete the nano.tgz file it leaves in your root directory. Your /opt tree will already contain the necessary files for nano.