The X-ray mission Chandra has observed a dramatic X-ray flare - a brightening by a factor of 50 for only three hours - from Sgr A*, the Galactic Center supermassive black hole. Sgr A* has never shown variability of this amplitude in the radio and we therefore argue that a jump of this order in the accretion rate does not seem the likely cause. Based on our model for jet-dominated emission in the quiescent state of Sgr A*, we suggest that the flare is a consequence of extra electron heating near the black hole. This can either lead to bulk heating of thermal electrons to T_ e 6*1011 K and significantly increased synchrotron-self Compton emission, or result from non-thermal particle acceleration with increased synchrotron radiation and electron Lorentz factors up to gamma _e> 105. While the former scenario is currently favored by the data, simultaneous VLBI, submm, mid-infrared and X-ray observations should ultimately be able to distinguish between the two cases.