[Exim] local delivery with no domain

I am running exim on a small LAN and want to use it for local delivery.
Is it possible to set exim up so that mail sent to simply "user" will
be redirected to "user@???" for delivery locally - to save
typing in the whole address for quick local mails we are always sending
off.

Many thanks in advance - you guys were a great help last time!

Gregor