  In this Letter we study the phase diagram and the approach to the equilibrium
of Josephson junction arrays on a dice lattice for two different values of the
magnetic frustration ($f=1/2,1/3$). In both cases the array unedrgoes a
Berezinskii-Kosterlitz-Thouless like phase transition. For the fully frustrated
array, $f=1/2$, we find evidence of a {\em glassy behavior} although the system
has {\em no disorder}. For comparison we study dynamics of the array at a
different value of frustration ($f=1/3$) and find no trace of glassy dynamics.
