Hmmm, my FreeBSD man page says different:
NAME
chroot - change root directory
...
DESCRIPTION
Dirname is the address of the pathname of a directory, terminated by an
ASCII NUL. Chroot() causes dirname to become the root directory, that
is, the starting point for path searches of pathnames beginning with `/'.
In order for a directory to become the root directory a process must have
execute (search) access for that directory.
It should be noted that chroot() has no effect on the process's current
directory.
Warner