2 things you need to be aware of;
1. You only get X number of days to 'open a dispute' via paypal. Once the dispute is opened, you get a further X number of days to escalate from dispute to claim. This is a very rigid system - and paypal don't give a fiddlers if you try to work outside of these parameters - so make sure your working within those guidelines.
2. You mention credit card company. Was the transaction made without logging into a (i.e. your) paypal account over visa/mastercard? If so, then you have an opportunity also to claim through them (but paypal is your first port of call). That is ONLY if you paid without actually logging into a paypal account. If you logged in to paypal to 'fund' paypal - which in turn, paid the vendor - then the credit card company will wash their hands of it. Even if the former, the credit card company may well try and wash their hands of it - but stand your ground - and keep the pressure on them until they relent (as they should do).