This is all you know, maybe any brothers, sisters, sons names, etc.? If he emigrated to the USA you could check also passenger list on Ellis Island page:
Possible Polish name of Czarnowsky is Czarnowski, and this is quite popular name in Poland.
CZARNOWSKI: root here is adj. czarny (black); it is a Polish surname which originated as a toponmyic tag form such localities as Czarnów, Czarnowo, Czarnówek or similar (Blackville, Blackly, Blackborough, Blackton - take your pick).
If the name were Czech or Slovak it would have been spelt Čarnovsky. If it was transltierated Russian/Ukrainian then it would be Charnovsky. Czarnowsky is a wierd hybrid.