You can add in the chain just fine. If it's a Shimano chain just get one of the new assembly snap off pins and install as per instructions. If it's a chain with a master link you have two options. One is to get another master link to join in the new segment. The other is to try using the chain tool to push a pin out most of the way and then push it back in again to join in the new segment. If you do it this way a nice job is quite possible but you want to watch now the pin is pushing back in. If it seems like it's getting cockeyed release the pressure and recenter the push pin on the chain pin so you can push the pin in as inline as you can make it. Otherwise you risk bruising and deforming the plates and it make not hold the pin well enough and you're looking at a future chain failure if it's not done well. It's not hard to do, you just need to use some attention and be quite critical with doing it right.
You'll need to push it through the other plate just a hair extra. And I do mean a hair. Then turn it around and give it just a hair of a push so the exposed ends of the pushed in pin are even with all the other exposed ends on both sides. The link should be easy to move now just like the others.