Hello I think you may be talking about a town that is no longer in Russia, but rather was in the Russian empire at the time your ancestor's record was created. In Belarus there is a town Delyatichi (Alternate names: Delyatichi [Rus], Delatycze [Pol], Delatitch [Yid], Dzialacičy [Bel], Delyatyche, Dzjaljacicy.) - I would say with almost 100% certainty that this is the town you're looking for! This was a shtetl in the Minsk Province of Belarus. If you're doing research on a Jewish family member then you should explore these links below:

http://www.jewishgen.org/Communities/community.php?usbgn=-1942336

http://www.iajgsjewishcemeteryproject.org/belarus/delyatichi-minsk.html

This shtetl is often lumped in with nearby Lyubcha, Belarus

I think you may be talking about a town that is no longer in Russia, but rather was in the Russian empire at the time your ancestor's record was created. In Belarus there is a town Delyatichi (Alternate names: Delyatichi [Rus], Delatycze [Pol], Delatitch [Yid], Dzialacičy [Bel], Delyatyche, Dzjaljacicy.) - I would say with almost 100% certainty that this is the town you're looking for! This was a shtetl in the Minsk Province of Belarus. 

If you're doing research on a Jewish family member then you should explore these links below:

http://www.jewishgen.org/Communities/community.php?usbgn=-1942336

http://www.iajgsjewishcemeteryproject.org/belarus/delyatichi-minsk.html

This shtetl is often lumped in with nearby Lyubcha, Belarus