RFID can be used for a variety of applications, e.g., to conveniently pay for public transportation. However, achieving security and privacy of payment is challenging due to the extreme resource restrictions of RFID tags. In this paper, we propose PSP -- a secure, RFID-based protocol for privacy-preserving payment. Similar to traditional electronic cash, the user of a tag can pay access to a metro using his tag and so called coins of a virtual currency. With PSP, tags do not need to store valid coins, but generate them on the fly. Using Bloom filters, readers can verify the validity of generated coins offline. PSP guarantees privacy such that neither the metro nor an adversary can reveal the identity of a user or link subsequent payments. PSP is secure against invention and overspending of coins, and can reveal the identity of users trying to doublespend coins. Still, PSP is lightweight: it requires only a hash function and few bytes of non-volatile memory the tag.