Building i386 Disk on AMD64 -- chroot Fails: Exec format error

["Matt Miller" <debian@mattmillersf.fastmail.fm>]

I've attached an external hard drive to my etch AMD64 box, and I want to
build an etch i386 system on it.  I partitioned the drive, and used
debootstrap to lay down a minimal i386 system on the drive.  The problem
is that I want to chroot into that system to do some more stuff, but the
chroot fails:

mmiller@xpc1:~$ sudo chroot /mnt/debinst /bin/bash chroot: cannot run
command `/bin/bash': Exec format error

So, what's next?  Don't I need to be able to get into that i386 system
and install a kernel and do some other things?  Can this type of cross-
system build be done?