We introduce the concept of supersymmetric laser arrays that consist of a main optical lattice and its superpartner structure, and we investigate the onset of their lasing oscillations. Due to the coupling of the two constituent lattices, their degenerate optical modes form doublets, while the extra mode associated with unbroken supersymmetry forms a singlet state. Singlet lasing can be achieved for a wide range of design parameters, either by introducing stronger loss in the partner lattice or by pumping only the main array. Our findings suggest the possibility of building single-mode, high-power laser arrays and are also important for understanding light transport dynamics in multimode parity-time symmetric photonic structures.