Hello Jaggerlock,
Yes, once you choose the premium membership option you want to subscribe for on the membership page at http://www.chess.com/membership.html and continue on to the next page you should see an option you can select to pay for the premium membership through Paypal.
Sorry for not searching this but my browser is running into some serious problems and net is slow so i decided to just ask here. Can you renew membership with paypal?