I've just heard that there will be a hard fork... so you get coins of a new cryptocurrency for every old coin... what is the name of the new cryptocurrency then? Will the old chi coins become worthless after the hard fork? Or did I understand something completely wrong here..

And where do I get the new coins??
You won't get any new coins, your old CHI will be the new CHI

All you have to do, is, to update your wallet. You should do this preferrably before the hardfork happens at block 440000 (we are at ~412000 now). An update at a later point is still possible though, as long as you don't use the chain in the meantime. But better to do it right away now so you are safe and won't forget it.
If you fail to update your wallet, you will either stop downloading blocks or be on a fork and you may lose coins, if you try spending/sending them.