The nonresonant nonlinear optical response of bulk tellurium (Te) is studied using 220 fs 10 µm laser pulses with photon energy roughly three times smaller than the band gap energy. The Kerr nonlinearity is found to be extremely large (n2,eff = 3.0-6.0 × 10-12 cm2/W), nearly 100 times larger than that of GaAs, depending on crystal orientation. Multiphoton absorption is observed at intensities >109 W/cm2 indicating the importance of free carriers to the overall nonlinear optical response. The large values of the nonlinear susceptibilities of Te open up possibilities of designing thin film elements for mid- and long-wavelength infrared nonlinear photonics.