We report on the first observation of dineutron emission in the decay of 16Be. A single-proton knockout reaction from a 53 MeV/u 17B beam was used to populate the ground state of 16Be. 16Be is bound with respect to the emission of one neutron and unbound to two-neutron emission. The dineutron character of the decay is evidenced by a small emission angle between the two neutrons. The two-neutron separation energy of 16Be was measured to be 1.35(10) MeV, in good agreement with shell model calculations, using standard interactions for this mass region.