The general consensus is no it is not required in Linux. However if you share files with a windows PC or run and Webserver or Email server or anything else that interacts with windows then it is worth running a Virus scanner just to stop from spreading Windows viruses.
There are, or were some Linux viruses see here and if you want to install an Antivirus program then ClamAV is free and available in the Ubuntu Software Centre. I was when i left the windows world for linux a little uncomfortable at not having an Antivirus program installed and so i did and do still install ClamAV on every Linux install, although it doesn't always run.
Here is a link to an explanation about the problem of viruses on Linux.
As with most OS's now days you are at most risk when on web sites as the web browsers launch helper programs which also help the viruses. But on most Linux's if something want's to install it needs your admin password so if you are not trying to install something and something asks for your password be suspicious. Also on Linux as most of the software you need is in it repository you are not in general installing software that you downloaded off of an unknown web site, so reduced risk.
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