  We give predictions for the neutrinoless double beta decay rate in a simple
variant of the A_4 family symmetry model. We show that there is a lower bound
for the neutrinoless double beta decay amplitude even in the case of normal
hierarchical neutrino masses, corresponding to an effective mass parameter
|m_{ee}| >= 0.17 \sqrt{\Delta m^2_{ATM}}. This result holds both for the CP
conserving and CP violating cases. In the latter case we show explicitly that
the lower bound on |m_{ee}| is sensitive to the value of the Majorana phase. We
conclude therefore that in our scheme, neutrinoless double beta decay may be
accessible to the next generation of high sensitivity experiments.
