PbS quantum dots of the average size 10 nm are synthesized in the polymer matrix (PVA) following chemical route. Optical absorption spectra reveal a large blue shift from the bulk absorption cutoff wavelength. Instead of using a high power laser, we have measured for the first time the third order nonlinear susceptibility (χ³) of PbS quantum dots using a low power continuous wave laser with the Degenerate Four Wave Mixing (DFWM) technique. The result is encouraging in nonlinear optical application at room temperature.