  Inverse Compton (IC) scattering is one of two viable mechanisms that can
produce the prompt gamma-ray emission in Gamma-Ray Bursts. IC requires low
energy seed photons and a population of relativistic electrons that upscatter
them. The same electrons can upscatter the gamma-ray photons to even higher
energies in the TeV range. Using the current upper limits on the prompt optical
emission we show here that under general conservative assumption the IC
mechanism suffers from an "energy crisis". Namely, IC will over-produce a very
high energy component that would carry much more energy than the observed
prompt gamma-rays. Our analysis is general and it makes no assumptions on the
specific mechanism that produces the relativistic electrons population.
