Mixers represent a good privacy preservation tool for many users. However, it always remains risky to rely on a centrally-operated service that can be compromised. And even they claim not to store details of opened sessions for more than 24h, it still poses a risk of being found out.
Unlikely, the best options mentioned by Theymos are not available for all of us. How many used the swap XMR/BTC to hide traces? Don't expected many!
If ChipMixer keeps logs (which you can't possibly know for sure), then they know exactly where the coins are coming from and going.
Does there any way to check if it really does?