Blind signatures allow a signer to digitally sign a document without being able to glean any information about the document. In this paper, we investigate the symmetric analog of blind signatures, namely blind message authentication codes (blind MACs). One may hope to get the same efficiency gain from blind MAC constructions as is usually obtained when moving from asymmetric to symmetric cryptosystems. Our main result is a negative one however: we show that the natural symmetric analogs of the unforgeability and blindness requirements cannot be simultaneously satisfied. Faced with this impossibility, we show that blind MACs do exist (under the one-more RSA assumption in the random oracle model) in a more restrictive setting where users can share common state information. Our construction, however, is only meant to demonstrate the existence; it uses an underlying blind signature scheme, and hence does not achieve the desired performance benefits. The construction of an efficient blind MAC scheme in this restrictive setting is left as an open problem*.