Sounds like a local virus issue. You should scan your computer for virus/malware issues.
What is Afr.php?

Users across several different websites are experiencing this problem, using a variety of browsers. The main recommendation is to clear your browser cache (and possibly delete your internet temporary files as well).
It is thought to be related to ads. Have you noticed it in connection with any specific ad being displayed?

It is a glitch in website. Don't download, there is no harm by cancelling download. Report the problem to Help & Support <---using this link or use link at bottom of the page. Include as complete and as many details as possible (exact date & time, what pages were open, exactly what you were doing, chatting on meebo, etc). They will quickly respond to your report.
edit--and also what artfizz says

Sometimes user's may be open to viruses by the Ads. Chess.com is around 99% Sure that all ads are ok though they have to load a code which slows down your process of loading pages to defeat this problem get a Membership :D I would recommend that you check for virues now :) If you get a membership there are no ads.
Whenever I try to chat with my friends or sometimes while loading a game, I see a download notification which attempts to download a file named afr.php to my documents folder or my windows. Can anyone please clarify the issue? Is there any harm done if that file is not downloaded at all?