A quasi-two-dimensional layer of MoS₂ was placed on top of a silicon optical waveguide to form a MoS₂–silicon hybrid structure. Chirped pulse self-phase modulation measurements were carried out to determine the optical Kerr nonlinearity of the structure. The observed increase in the spectral broadening of the optical pulses in the MoS₂–silicon waveguide compared with the silicon waveguides indicated that the third-order nonlinear effect in MoS₂ is about 2 orders of magnitude larger than that in silicon. The measurements show that MoS2 has an effective optical Kerr coefficient of about 1.1 × 10^?16 m²∕W. This work reveals the potential application of MoS₂ to enhance the nonlinearity of hybrid silicon optical devices.