A new mechanism for primordial melting of chondrules based upon heating by relativistic electrons accelerated by reconnecting magnetic field lines is discussed. This mechanism is free of the creation-annihilation problem of collisions used for heating. The basic requirements for reconnection are an interplanetary magnetic field with regions of reversals. An early mangetic field is inferred from the paleomagnetism of meteorites and the requirements of solar spin-down, while the field reversals upon which the reconnection is based are a common property of the present epoch solar wind.