I'm running Vista Business x86 and thinking of upgrading my single core
CPU to a dual core CPU. Will this be transparent to the operating system
or will a repair be necessary?

If you're just replacing the CPU on the same motherboard,
the system will work, but only with one core. At minimum,
a repair install would be necessary, and might be successful,
but a full clean install may be required, and is the better option.

If your single core CPU is a P4 with HT, no change will be
necessary.

Thanks for the replies. I was afraid that it was not going to be possible
to enable multi-core functionality in the current OS install. That does put
a damper on things.