I'm currently trying to set up a chroot jail on my Fedora 15 machine.

I tried a minimal approach first only putting the necessary files in it. However, the tty command tells me "not a tty". I then tried adding hard links to all kinds of different system directories like /dev, /var, /etc, /tmp to it, but to no avail.
I even made the chroot directory a hard link to / but tty still tells me "not a tty". So what I'm getting, is that just hard linking the necessary directories and files doesn't do it.
What do I need to do to get a real tty in my chroot jail?

You should not hardlink directories; bind-mount them:
Have you mounted /proc inside the chroot? You probably need to. You also need to have /dev/ptmx and /dev/pts/ (latter mounted), if you wish to use pseudoterminals inside the chroot. If you don't, tty will always report 'not a tty'.