  We examine Bousso's covariant entropy bound conjecture in the context of
radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound
is violated near the big bang. However, the hope has been that quantum gravity
effects would intervene and protect it. Loop quantum cosmology provides a near
ideal setting for investigating this issue. For, on the one hand, quantum
geometry effects resolve the singularity and, on the other hand, the wave
function is sharply peaked at a quantum corrected but smooth geometry which can
supply the structure needed to test the bound. We find that the bound is
respected. We suggest that the bound need not be an essential ingredient for a
quantum gravity theory but may emerge from it under suitable circumstances.
