First, install the primary key - it can then be used to install our keyring and mirrorlist.
$ pacman-key --recv-key FBA220DFC880C036 --keyserver keyserver.ubuntu.com
$ pacman-key --lsign-key FBA220DFC880C036
$ pacman -U 'https://cdn-mirror.chaotic.cx/chaotic-aur/chaotic-keyring.pkg.tar.zst' 'https://cdn-mirror.chaotic.cx/chaotic-aur/chaotic-mirrorlist.pkg.tar.zst'
Append (adding to the end of the file) to /etc/pacman.conf:
[chaotic-aur]
Include = /etc/pacman.d/chaotic-mirrorlist