Do I need to change the timing chains?

You are correct. The timing chain has a stretched area in it where it is stretched out longer than the rest of the chain and that is why it tightens and loosens. Sometimes chains needs re-adjustment after turning the motor when putting timing chains on. In fact, this is what should be done to make sure the timing marks still line up after the engine is returned to top dead center on cylinder number one to assure that the chain is on the correct tooth. Do the timing marks still line up when the crank is returned to TDC of the nuber one cylinder? If it is a twin cam one of the cams may need to be moved to line up the timing marks. That is the only thing that could be another possibility. Otherwise the chain does need replacement and it is a good time to do it anyway since you have it apart. Get a timing chain kit which will come with timing chain components like the tensioner and idler puley and good kits will come with a water pump and accesory belts. You can use the search engine on this site to bring up retailers who sell kits. Just look at the links and banners that come up on the page. It is also location optimized and you may find a retailer near you.