Don't even think about it! The owl was Athene's sacred bird, and nobody--especially an Athenian--would even consider offering one up for sacrifice. Owls were so sacred and protected in Athens that there was a common cliché about "owls to Athens." The modern equivalent would be bringing "coals to Newcastle." In case you're not familiar with the "coals to Newcastle" phrase, it comes from the fact that Newcastle is a coal-producing region in Britain. Thus, if you were to bring coals to Newcastle (or owls to ancient Athens) you would be indulging in an unnecessary effort, similar to transporting an item to some place that already had an excess of items just like it.

More cynical scholars interpret this phrase as a jibe at the Athenians' obsessive accumulation of weath, since Athene's owl appeared on their coins, but that's a whole nother can of worms.