Run nix as user in a lightweight chrooted container.

$ mkdir -m 0755 ~/nix && chown $(whoami) ~/nix
$ nix-user-chroot ~/.nix sh
$ download and extract latest nix binary tarball
$ nix-*-linux/install

You are in a user chroot where / is owned by your user, hence also /nix is owned by your user. Everything else is bind mounted from the real root.

Notes:

• The nix config is not in /etc/nix but in /nix/etc/nix, so that you can modify it. This is done with the NIX_CONF_DIR, which you can override at any time.
• It requires user namespaces, at least Linux 3.8.