How to let the user execute a command containing quotes in sudoers?

The simple solution is to put your command in a script and then give your users access to the script via sudo.

user ALL = (root) NOPASSWD: /path/to/yourscript

Then

#/bin/bash
chroot /chroots/box /bin/bash -c 'cd /repos/system && git pull'

Ensure that your users do not have write access to yourscript.

edit: Warning, it appears that sudo does not safely handle spaces in the command, so it is not safe to use sudo in this way. https://unix.stackexchange.com/a/279142/39281

Instead of using quotes in the sudoers file, you can escape spaces using backslash:

user ALL = (root) NOPASSWD: chroot /chroots/box /bin/bash -c cd\ /repos/system\ &&\ git\ pull

You can still use it as follows, because the user's shell handles the quoted argument anyway:

chroot /chroots/box /bin/bash -c 'cd /repos/system && git pull'

Personally I like the other answer, to put it in a script, but this answers the actual question.