GPL/LGPL and the Linux kernel

We were talking liscening issues here today and I was asked a question.

If the linux kernel is under the GPL, it can be linked against glibc
without a problem.

Now let's say that I write a non-GPL compatible program and want to run
it on Linux. If it links against the kernel then I am in volation of
the GPL'ed kernel liscense - correct. If so, how do I run my program on
linux?

sps