Two things I can think of :
Search around the web and see if you can dig up some review on the case or a website selling the case which provides details about the chipset.
Open the case and have a look at the chipset yourself,
The website showing above mentions something which might actually be the chipset used :
I don't know enough about external cases to tell though. Might be a better idea to do a search for those two items instead and see if they are the chipset of the case. If so, then you don't need to go around trying to figure out the chipset of the case.