We have studied parametric amplification in dispersion-engineered ${\mathrm{As}}_2{\mathrm{S}}_3$ waveguides achieving a highest gain of over $+35\mathrm{dB}$ using a pulsed pump. The gain is shown to involve an interaction between stimulated Raman scattering (SRS) and four-wave mixing (FWM). The gain was studied both experimentally and using computer modeling, which revealed that SRS contributes over $+20\mathrm{dB}$ to the combined gain and significantly modifies the dependence of the FWM the conversion efficiency as a function of propagation distance and dispersion. The implications for FWM using low-power CW beams are discussed.