How can Peggy prove she knows one of Victor's passwords in zero knowledge?
Yes, there is. 

Assuming Peggy and Victor will be honest about their inputs, they can achieve exactly this functionality with garbled circuits. Victor can generate a circuit which will check for equality between Peggy's input and his list of passwords, then he proceeds to garble the circuit. Victor and Peggy cooperate in oblivious transfers for Peggy to get the circuit keys related to her input and she proceeds to evaluate the garbled circuit. She returns her output to Victor who can then clearly see whether or not the input Peggy provided is actually equal to one of his passwords, and he does not know which one. Such a protocol can be made maliciously secure as well. 

It can also be implemented with secret sharing as well as other secure multiparty computation algorithms, but garbled circuits is usually one that is fairly intuitive for many.