Abstract: Any smooth plane quartic can be reconstructed from its bitangents. It is known since ancient times (the 1860's) that any smooth plane quartic has exactly 28 bitangents. A long standing question from that era is: "given only the set of 28 bitangents to a smooth plane quartic, can one reconstruct the quartic?". We use an isomorphism of two moduli problems, and the recent classification of 2-transitive groups, to give an affirmative answer to this question.