For a project such as OpenVZ, security of the software is of paramount importance. Let's explain how we assure that OpenVZ is secure.
The OpenVZ kernel is based on the Linux kernel. The OpenVZ team tracks and analyzes all the security updates to the Linux kernel and applies them accordingly.
To achieve the maximum possible security and stability, stable OpenVZ kernels are based on Red Hat Enterprise Linux kernels, which are conservative and well-maintained. By using an enterprise kernel as a base (rather than latest vanilla kernel), we avoid adding new bugs or security holes, still the old ones are getting discovered and fixed, and the kernel matures.
OpenVZ has undergone a thorough security audit, performed by Solar Designer in winter 2005. He found a single issue in OpenVZ kernel code and a couple of issues in mainstream Linux kernel code — all of them were fixed, and the mainstream fixes were sent to the LKML.