Yes, you can do this.
You have not specified the version of Linux you are using but if it is CentOS6 (or Redhat or Fedora etc), KVM is possibly your best bet. [ Same probably applies for other Distros but Redhat has thrown its weight behind KVM, and KVM does deliver ].
In order to support virtualization you need a 64 bit version of Linux running on it run the command
egrep '(vmx|svm)' --color=always /proc/cpuinfo
If it finds one of these, it means your hardware is capable of running KVM. (You may need to enable Virtualization Support in your BIOS). Once you are running KVM you can run pretty much any version of Linux you like - you may even be able to run Windows - but I've never tried that.
Before going to all that work though, are you sure you can't simply disable "secure boot" in the bios - I was under the impression that this was standard practice.