It looks like you have a hot-air gun. This should make the process fairly painless. (Unless you touch something hot, of course!)
I would try to suspend the board to ensure the component isn't touching anything. Then heat up the pins on the back of the board with your hot air gun. When the solder melts, the component's weight should cause it to fall away from the board.
One pin looks like it's tied directly to the ground plane, and a few others might be tied to a copper fill on the component side of the board. These will require a lot of heat: the whole plane needs to get hot before the solder joints will melt.
If the solder melts but the chip doesn't fall off, I recommend poking the pins with a thin wooden dowel (or a toothpick). The wood might start to smolder, but I haven't had one catch fire yet :)