I've pulled many chips from old machines and never cracked a socket. You need to use a very small thin flat screwdriver (a watch repair one is ideal, as already suggested) and ideally you want to apply most of the pressure upwards on the chip rather than down on the socket... and you only need to loosen it enough to pull the chip by hand.
A chip puller is ideal, but for most chips you can get by with a screwdriver. Chip pullers are also pretty easy to improvise from thin flat pieces of metal. I've seen it even done effectively with 2 bent paperclips.
Note that with PLCC type chips where the sockets are level with the top of the chips (rather than the chip lying almost entirely above the socket, as with say the Kickstart ROMs or 68000 in an Amiga) you would be kind of dumb to try and pry the chip out. Aside from cracking the socket, youre likely to damage the chip leads too.
I think the chip he's trying to yank out is of the other sort though, in which case levering a screwdriver under the chip and above the socket is perfectly acceptable.
