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The recent discovery of day-long gamma-ray flares in the Crab Nebula,presumed to be synchrotron emission by PeV (10^{15} eV) electrons in milligaussmagnetic fields, presents a strong challenge to particle acceleration models.The observed photon energies exceed the upper limit (~100 MeV) obtained bybalancing the acceleration rate and synchrotron radiation losses under standardconditions where the electric field is smaller than the magnetic field. Weargue that a linear electric accelerator, operating at magnetic reconnectionsites, is able to circumvent this difficulty. Sufficiently energetic electronshave gyroradii so large that their motion is insensitive to small-scaleturbulent structures in the reconnection layer and is controlled only bylarge-scale fields. We show that such particles are guided into thereconnection layer by the reversing magnetic field as they are accelerated bythe reconnection electric field. As these electrons become confined within thecurrent sheet, they experience a decreasing perpendicular magnetic field thatmay drop below the accelerating electric field. This enables them to reachhigher energies before suffering radiation losses and hence to emit synchrotronradiation in excess of the 100 MeV limit, providing a natural resolution to theCrab gamma-ray flare paradox.

Reconnection-Powered Linear Accelerator and Gamma-Ray Flares in the Crab Nebula