Hmn, strange. It must be something in your installation or setup of Chrome, i and many others use Chrome exclusively and don't seem to have any issue with it. In fact usually when there is an issue it's with firefox and the advice is to use Chrome because it's the most stable on this forum.
Do you have any extensions that might effect it? Is your virus protector stopping anything from running? The message shown usually happens because you're not allowing the login session cookiees to be saved for the site, is your cookiee setting too high? Is your security suite blocking cookiees?
i7 7700,k NV1070 8GB, 16GB 3200mhz memory, 1x 2TB Hybrid, Win10.
i5 4760k, NV960 2GB, 16GB 2333mhz memory, 1x 2TB Hybrid, Win10.
i5, NV1050 4GB, 8GB memory, 1x 1TB HDD, Win10.
i3, Intel 4000 series graphics, 6GB memory, 1x 500gb HDD, Win8.1.