Zonal (latitudinal) winds dominate the bulk flow of planetary atmospheres. For gas giant planets such as Jupiter, the motion of clouds can be compared with radio emissions from the magnetosphere, which is connected to the planet's interior, to determine the wind speed. In principle, this technique can be applied to brown dwarfs and/or directly imaged exoplanets if periods can be determined for both the infrared and radio emissions. We apply this method to measure the wind speeds on the brown dwarf 2MASS J10475385+2124234. The difference between the radio period of 1.751 to 1.765 hours and infrared period of 1.741 +/- 0.007 hours implies a strong wind (+650 +/- 310 meters per second) proceeding eastward. This could be due to atmospheric jet streams and/or low frictional drag at the bottom of the atmosphere.