Layered antiferromagnetism is the spatial arrangement of ferromagnetic layers with antiferromagnetic interlayer coupling. The van der Waals magnet chromium triiodide (CrI3) has been shown to be a layered antiferromagnetic insulator in its few-layer form(1), opening up opportunities for various functionalities(2-7) in electronic and optical devices. Here we report an emergent nonreciprocal second-order nonlinear optical effect in bilayer CrI3. The observed second-harmonic generation (SHG; a nonlinear optical process that converts two photons of the same frequency into one photon of twice the fundamental frequency) is several orders of magnitude larger than known magnetization-induced SHG(8-11) and comparable to the SHG of the best (in terms of nonlinear susceptibility) two-dimensional nonlinear optical materials studied so far(12,13) (for example, molybdenum disulfide). We show that although the parent lattice of bilayer CrI3 is centrosymmetric, and thus does not contribute to the SHG signal, the observed giant nonreciprocal SHG originates only from the layered antiferromagnetic order, which breaks both the spatial-inversion symmetry and the time-reversal symmetry. Furthermore, polarization-resolved measurements reveal underlying C-2h crystallographic symmetry-and thus monoclinic stacking order-in bilayer CrI3, providing key structural information for the microscopic origin of layered antiferromagnetism(14-18). Our results indicate that SHG is a highly sensitive probe of subtle magnetic orders and open up possibilities for the use of two-dimensional magnets in nonlinear and nonreciprocal optical devices.