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There is a seeming paradox if you try to introduce magnetic monopoles into a chiral gauge theory, including the Standard Model. The chiral nature of the theory means that the ingoing scattering modes carry different quantum numbers from the outgoing modes. The challenge is to find a way to consistently turn the ingoing modes into outgoing modes while preserving the gauge symmetries. The seeming paradox is that there is no way to do this. I will review this paradox and explain ideas on how to resolve it.