For the project such as OpenVZ, security of the software is of paramount importance. This is how we assure that OpenVZ is secure.
Kernel
The OpenVZ kernel is based on the Linux kernel. OpenVZ team is tracking and analyzing all the security updates to the Linux kernel and applies them accordingly.
Note that current stable kernel branch is based on 2.6.8 kernel, which is quite old. This is done to achieve maximum possible security and stability. By using the older kernel, we do neither add new bugs nor security holes, but the old bugs and holes are getting discovered and fixed, and the kernel matures. Big vendors such as Novell and Red Hat are doing the same for their enterprise Linux offerings: for example, Red Hat Enterprise Linux 4 is based on kernel 2.6.9.
Audit
OpenVZ has undergone a throughtout 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 there fixed, mainstream fixes were sent to LKML.