This is a two part question:

a.  Is it possible for a person to be granted a Secret level security
clearance if they have dual citizenship with a "US-friendly" country
(say, for instance, Australia or New Zealand) and not have to renounce
their citizenship?

b. If it is possible, how much of a wrench will this throw into the
equation?  Obviously, clearances are not granted in a vacuum, and a
whole host of issues and potential concerns are considered.  That
said, if everything else were in order, how important a factor is the
dual citizenship issue considered?