When the OOB or Custom Unsubscription link is clicked in Chrome, It displays message Loading..... and even when you click on Validate button nothing happens.
It works fine in Internet Explorer.
Below is the screenshot
Can you enable the Chrome Developer Tools (Ctrl+Shift+I) and review the console and network tabs when hitting the unsubscribe? This should provide further insight into what is going on. This sounds like a coding issue within the page itself since it works with one browser but not the other, but you'll need to review the responses within the developer tools and compare it with the page source code.