The nonlinear properties of a low loss hydrogenated amorphous silicon core fiber have been characterized for transmission of high power pulses at 1540 nm. Numerical modelling of the pulse propagation in the amorphous core material was used to establish the two-photon absorption, free-carrier absorption and the nonlinear refractive index, which were found to be larger than the values typical for crystalline silicon. Calculation of a nonlinear figure of merit demonstrates the potential for these hydrogenated amorphous silicon core fibers to be used in nonlinear silicon photonics applications.