A lot depends on the quality of the chain link and what predators you have in your area. Small predators such as rats and weasels can easily pass right through the openings in chain link. If the chain link is lower quality or improperly installed, dogs and even large raccoons could pull it apart and create a hole large enough to get in. Even with a properly installed high quality chain link fence, if the chickens are close enough to the fence raccoons can reach through the fence and pull them out piece by piece (yes, it really is as gruesome as it sounds). Also, chickens can (and do) stick their heads through chain link to pick at things on the other side of the fence which can leave them vulnerable to predators grabbing them and pulling them through the fence (sadly, chickens aren't always as alert to danger as they should be).
I would at least put chicken wire around the bottom 2-3 feet of fence to reduce the risk of reach through predation (raccoons can still get through, but the chicken wire will slow them down a little and hopefully the chickens will be clever enough to move away from the fence). Unless you have weasels/mink in your area that will probably be adequate, but it still isn't predator proof. If you do have weasels I would recommend saving up the money for hardware cloth.