Ok so hypothetically, if I had Ubuntu 64-bit running on my computer with an AMD64 processor(Athlon 64 3200+ Venice), I could run x86 binaries, without an i386 chroot?
Debian (and derivative distros, eg. Ubuntu, Knoppix), Gentoo and some other distributions do not provide the 32bit libraries by default - you need to install them (the mentioned above compatibility libraries). These libraries are provided in so-called ia32-libs packages in order to simplify things.
For example Mandriva and Red Hat include those libraries in 64bit ports so you can run the 32bit programs with out any problems.
However in case of distros that don't include the 32bit libraries by default you may have problems even after installing ia32-libs - some programs require libraries that are not included in ia32-libs packages, but for majority of programs it should be enough.
In such case the chroot is the only way.
I once used amd64 port of Fedora (based on RedHat) and I had no problems running 32bit programs.
Now I use Debian amd64 and I chose 'the chroot way' because I have also a 32bit Debian installed so I didn't have to install the chroot - I just chroot to the other Debian if I need to run 32bit apps. Thus I don't know which 32bit programs will run w/o chroot, but I heared that for example 32bit firefox (needed if you need win32 codecs and flash plugin) runs well with ia32-libs.
Moreover I wasn't able to run 32bit tremulous in the chroot so maby the ia32-libs will be just fine in your case.
So I suggest you to install the ia32-libs and to try it out.