A quasi-two-dimensional layer of MoS_2 was placed on top of a silicon optical waveguide to form a MoS_2–silicon hybrid structure. Chirped pulse self-phase modulation measurements were carried out to determine the optica Kerr nonlinearity of the structure. The observed increase in the spectral broadening of the optical pulses in the MoS_2–silicon waveguide compared with the silicon waveguides indicated that the third-order nonlinear effect in MoS_2 is about 2 orders of magnitude larger than that in silicon. The measurements show that MoS_2 has an effective optical Kerr coefficient of about 1.1 × 10~(-16)m~2∕W. This work reveals the potential application of MoS_2 to enhance the nonlinearity of hybrid silicon optical devices. A quasi-two-dimensional layer of MoS_2 was placed on top of a silicon optical waveguide to form a MoS_2-silicon hybrid structure. Chirped pulse self-phase modulation measurements were carried out to determine the optica Kerr nonlinearity of the structure. in the spectral broadening of the optical pulses in the MoS_2-silicon waveguide compared with the silicon waveguides indicated that the third-order nonlinear effect in MoS_2 is about 2 orders of magnitude larger than that in silicon. The measurements show that MoS_2 has an effective optical Kerr coefficient of about 1.1 × 10 ~ (-16) m ~ 2 / W. This work reveals the potential application of MoS_2 to enhance the nonlinearity of hybrid silicon optical devices.