Chorzów is almost Katowice, so take any express/IC/EC train and you should be there in about 3 hours, then take a tram (or bus or taxi) to your destination in Chorzów.
rozklad-pkp.pl/?q=en/node/143 - Timetables
Examples (Monday 27th July 2009):
7:58 from Warszawa Centralna, 10:54 in Katowice (EX = Express, 97 PLN)
9:25 from Warszawa Centralna, 12:07 in Katowice (EC = EuroCity, 100 PLN)
16:25 from Warszawa Centralna, 19:10 in Katowice (IC = InterCity, 107 PLN)
The indicated prices are for 2nd class, 1st class costs 34 PLN more.
You can also take a cheaper train (POS = Pospieszny) at for example 13:23, but then you travel 1 hr longer (17:23 in Katowice), but you'd pay only 50 PLN (or 77 PLN in the 1st class).
