We present an 8.5-hour simultaneous radio , X-ray , UV , and optical observation of the L dwarf binary 2MASSW J0746425+200032 . We detect strong radio emission , dominated by short-duration periodic pulses at 4.86 GHz with P = 124.32 \pm 0.11 min . The stability of the pulse profiles and arrival times demonstrates that they are due to the rotational modulation of a B \approx 1.7 kG magnetic field . A quiescent non-variable component is also detected , likely due to emission from a uniform large-scale field . The H \alpha emission exhibits identical periodicity , but unlike the radio pulses it varies sinusoidally and is offset by exactly 1/4 of a phase . The sinusoidal variations require chromospheric emission from a large-scale field structure , with the radio pulses likely emanating from the magnetic poles . While both light curves can be explained by a rotating mis-aligned magnetic field , the 1/4 phase lag rules out a symmetric dipole topology since it would result in a phase lag of 1/2 ( poloidal field ) or zero ( toroidal field ) . We therefore conclude that either ( i ) the field is dominated by a quadrupole configuration , which can naturally explain the 1/4 phase lag ; or ( ii ) the H \alpha and/or radio emission regions are not trivially aligned with the field . Regardless of the field topology , we use the measured period along with the known rotation velocity ( v { sin } i \approx 27 km s ^ { -1 } ) , and the binary orbital inclination ( i \approx 142 ^ { \circ } ) , to derive a radius for the primary star of 0.078 \pm 0.010 R _ { \odot } . This is the first measurement of the radius of an L dwarf , and along with a mass of 0.085 \pm 0.010 M _ { \odot } it provides a constraint on the mass-radius relation below 0.1 M _ { \odot } . We find that the radius is about 30 \% smaller than expected from theoretical models , even for an age of a few Gyr . The origin of this discrepancy is either a breakdown of the models at the bottom of the main sequence , or a significant mis-alignment between the rotational and orbital axes .