The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants(1,2). The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field(2); this 'anomalous' Hall effect is important for the study of quantum magnets(2-7). The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of timer-eversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external electric field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints(8-10). Here we report observations of the nonlinear Hall effect(10) in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment(10) of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in nonmagnetic quantum materials.