  We present an exploratory lattice QCD calculation of the neutrinoless double
beta decay $\pi\pi\to ee$. Under the mechanism of light-neutrino exchange, the
decay amplitude involves significant long-distance contributions. The
calculation reported here, with pion masses $m_\pi=420$ and 140 MeV,
demonstrates that the decay amplitude can be computed from first principles
using lattice methods. At unphysical and physical pion masses, we obtain that
amplitudes are $24\%$ and $9\%$ smaller than the predication from leading order
chiral perturbation theory. Our findings provide the lattice QCD inputs and
constraints for effective field theory. A follow-on calculation with fully
controlled systematic errors will be possible with adequate computational
resources.
