Just make sure the little metal hooks are fully underneath the chip, and you should be fine. Two ways to go from there -- you can squeeze the tool together (the plastic will eventually seat against the socket) and the chip will "pop" out, or you can try to gently wiggle it out a bit at a time. (I prefer the second method if possible.)
The last time I had to remove an Agnus, I was able to use the hooks to carefully lift the chip out a little at a time... absolutely no chance for damage that way. If the chip doesn't want to budge, you may have to give the tool a squeeze. Either way though, I've *never* (knock on wood) had a PLCC socket break on me.