Players of Massively Multiplayer Online games (MMOs) consume content much faster than game designers can produce it. However, they also generate stories through their interaction, which can contribute to adding novel types of content in the game world. We introduce and demonstrate Play Arcs, a design strategy for structuring emergent stories that players can codesign and contribute as unique game content. We develop an MMO with tools for co design and 'history game mechanics' and test as a technology probe with 49 players. We show that Play Arcs successfully structure coherent stories and support players in shaping new, unique content based on their own histories. We found that these stories can inform and guide players' decisions, and also that, while players often share simpler stories directly, they keep more notable stories to themselves for retelling later. We conclude by discussing design challenges and directions for future work with Play Arcs.