The Kingspyre Tower is one the largest and tallest of the towers of Harrenhal. The original name for the tower was lost when Harren the Black and his sons died during the War of Conquest. It received its new name when Aegon I had his dragon, Balerion, burn Harren and his sons alive in the tower. It is lopsided beneath the weight of slagged stone, the result of Balerion's dragonbreath.
A Clash of Kings
When Tywin Lannister takes the castle, he keeps his apartments in this tower.