How do you kill a big tree stump?

We had this giant Apple tree in our back yard and we were thinking about taking it down as it simply dropped sooooooo many apples it made the yard useless. It would start dropping apples in June and would drop them until the end of October. The apples never matured enough to use so it was a real waste. Last week the trunk split and cracked so it made the choice easy it had to come down. We got it down fine but now we have this huge stump... how do we get rid of it, any suggestions?