One of the strongest experimental indications of hydrogen tunneling in biology has been the elevated Swain - Schaad exponent for the secondary kinetic isotope effect in the hydride-transfer step catalyzed by liver alcohol dehydrogenase. This process has been simulated using canonical variational transition-state theory for overbarrier dynamics and optimized multidimensional paths for tunneling. Semiclassical quantum effects on the dynamics are included on a 21-atom substrate - enzyme - coenzyme primary zone embedded in the potential of a substrate - enzyme - coenzyme - solvent secondary zone. The potential energy surface is calculated by treating 54 atoms by quantum mechanical electronic structure methods and 5506 protein, coenzyme, and solvent atoms by molecular mechanical force fields. We find an elevated Swain - Schaad exponent for the secondary kinetic isotope effect and generally good agreement with other experimental observables. Quantum mechanical tunneling is calculated to account for ~60% of the reactive flux, confirming the dominance of tunneling that was inferred from the Swain - Schaad exponent. The calculations provide a detailed picture of the origin of the kinetic isotope effect and the nature of the tunneling process.