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The scaling and design principles for a MJ-scale krypton fluoride laser are derived and applied. First, the scaling limits of size and operation of a single large-aperture module (oscillator or amplifier) are explained, and its performance evaluated. A new scheme for combining amplifier modules into high output power chains is then presented. The performance of this architecture is investigated, showing that it effectively produces both the total energy and pulselength required for inertial confinement fusion using existing technology, while maintaining an easily manageable level of system complexity and acceptable low flux levels on optical elements.