I can personally guarantee that no virus is coming from Chordie. I have 100% control of the code of the site.
I do link to some other pages (as every other web page do). I can never guarantee that these sites are virus free, I do however always review the sites I link to.
Chordie do however set a couple of cookies (to remember password, and the remember the state of the menues when browsing artists). If you are scanning for malware, I have noticed that some of the programs(like adAware) are reporting cookies as a possible privacy problem.
You will however get this warning for all the sites where you can be automatically logged in - it is the only way to do it. This has nothing at all to do with viruses, and the only possible threat that it might pose, is that you little brother (using the same computer) might get access to your songbook collection on Chordie. If your brother is a really obnoxious little prat that might love messing around with your valuable songs, you might consider looging out of Chordie before leaving the computer.