Just be careful that you don't bend the pins of the new IC as you plug it in. Ensure that the pins are correctly located in the socket, before giving that final push.
Brand new DIP ICs have their pins slightly "splayed", and don't easily fit into DIP sockets. There are a couple of options here.
The easiest way is to get a DIP IC pin straightener; this is a tool into which you can pop the IC, give it a squeeze, and it will bend the pins back into place, and get rid of a lot of the "splay" too. It's great for when you have an IC with bent pens or such. The problem, though, is finding one. I've had the best luck via surplus electronics places, and hamfests. Then again, I haven't tried to source the tool new, so maybe one can still be had via a normal source of some kind?
The next way takes a bit of finesse and being really careful. Basically, you lay all the legs of the pin, on it's side, on a very flat surface. Keeping them all in contact with the surface, you gently "rock" the IC so that the pins all get bent by a little bit. Then do the other side.
This method is fairly easy to do with most 0.3" width ICs with few pins (like the ATMega328). On larger ICs (like the 0.6" width ones with a lot of pins - or behemoths like the "aircraft carrier" Motorola 68000 processor) it can be very difficult or impossible to do (without damage to the IC), just because of the sheer number of pins needing bending. In those cases, a tool is definitely called for.