I found an interesting YouTube video with a neat de-soldering trick that requires no special equipment.
Essentially you bend a reasonably thick piece of copper wire round into a right-angled S shape, add a layer of solder over the bottom edges, then place it over the chip. By heating the copper from the top, it melts the solder and provides a near perfect coverage of the IC's pins. From there you can just lift it off the board with tweezers.
Is this likely to work without damaging the IC or the board's pads, as described in the video?