  We show that a strongly interacting chain of Majorana zero modes exhibits a
supersymmetric quantum critical point corresponding to the $c={7\over 10}$
tricritical Ising model, which separates a critical phase in the Ising
universality class from a supersymmetric massive phase. We verify our
predictions with numerical density-matrix-renormalization-group computations
and determine the consequences for tunnelling experiments.
