PCT claiming priority of CIP

With all due respect Steven, Jean Jacques, Benjamin, I have to differ. The claim to priority is valid (claim to the first patent application means the first application in which that invention with its CIP limitations was disclosed) - it simply means that your PCT is imputed the date of the CIP. Therefore any earlier application that gets published (in this case the parent) will be prior art.
Remember that the PCT is a placeholder for subsequent nationally and regionally prosecuted patent applications. Those jurisdictions will look at the prior art available prior to the CIP date (since your PCT claimed priority from the CIP). Therefore it comes down to the claim language. Insofar as your claims are novel and inventive/non-obvious over the parent case (in other words the limitations provided by the CIP are not obvious in light of the published parent case), your claims should be allowed in subsequent national and regional applications.