The short answer to your question is no, The Chromebook does not require an anti-virus.
The reason for this is that Chromebook is based on Linux but is designed in a way that makes it almost impossible to install something on your device that might jeopardise its safety.
Chromebook and Anti-virus
The thing that makes Chromebook different from most laptops is that it only allows you to use web-based applications, therefore it is safer by default - at least as safe as the websites you are using!
Once you restart your computer, or simply shut it down, the next time you start it it will be restored to it's default settings and work just as it did before.
It is also very easy, on the off chance that something does go wrong, to restore your Chromebook back to it's factory settings.
This makes is far less vulnerable to viruses, reducing the need to use anti-virus software on a Chromebook.
That's not to mean you can't run cloud-based antivirus software if you choose.. but it's an option not many Chromebook users bother with to be honest!
