That would be nice to have as a built-in functionality, but apparently it differs from mod_chroot.
I have added "ChrootDir /var/www" to /etc/apache2/conf.d/my_defaults, but it seems like the fastcgi processes now get started outside of the chroot / before Apache chroots:
I am getting the following error (only /var/www/usr/lib/libc-client.so.2007e exists, not /usr/lib/libc-client.so.2007e):
/var/www/bin/php4-fcgi: error while loading shared libraries: libc-client.so.2007e: cannot open shared object file: No such file or directory
Apart from that there appears to be another problem, fastcgi processes (PHP) return "Service Temporarily Unavailable", while requests to normal resources (image) work fine.
This is likely also related to the order in which chrooting and spawning the fastcgi processes happens.
I am using mod_fastcgi.