"Google... said users would no longer have to worry about viruses, malware and security updates"

I'm guessing since most applications on Chrome will be web-based, the vendor will worry about them. They will be able to more easily and quickly detect + destroy phishing schemes, viruses etc. Kind of like how Facebook has responded to malicious wall posts.

For me the bigger concern would be the loss of productivity due to downtime of web services, or loss of internet connectivity.