  We show that a new glassy phase can emerge in presence of strong magnetic
frustration and quantum fluctuations. It is a Valence Bond Glass. We study its
properties solving the Hubbard-Heisenberg model on a Bethe lattice within the
large $N$ limit introduced by Affleck and Marston. We work out the phase
diagram that contains Fermi liquid, dimer and valence bond glass phases. This
new glassy phase has no electronic or spin gap (although a pseudo-gap is
observed), it is characterized by long-range critical valence bond correlations
and is not related to any magnetic ordering. As a consequence it is quite
different from both valence bond crystals and spin glasses.
