We report for the first time the determination of the real part of the third order nonlinear susceptibility χ(3)(-ω;ω,0,0) above the nematic to isotropic phase transition temperature of a nematic liquid crystal 4 (trans-4'-4'-n-pentylcyclohexy)-benzonirtile (PCH-5) from electro-optic Kerr effect experiments. The value of χ(3) observed at 632.8 nm is found to be 6.2079×10-19 m2 V -2 close to the phase transition temperature at 55.1°C.