Based on density functional calculations in combination with empirical corrections for the van der Waals interaction, we show that a recently synthesized two-dimensional sheet of π-conjugated Ni bis(dithiolene) complex (NiC4S4) exists in the form of bilayers with specific pairs of interlayer covalent bonds rather than in the form of isolated single layers. When one of the layers is slid relative to the other in the direction diagonal to two primitive vectors by applying a shear stress of ∼135 pN between the two layers brings about a gradual decrease in the band gap from 0.15 to 0 eV. Unlike in the case of an isolated single layer, the band gap of the bilayer is always found to be direct during the change. Therefore, the (NiC4S4)2 bilayer will be quite useful in nanoelectromechanical devices as well as in optoelectronic devices.