Given the fine-scale temperature and salinity in an actively convecting thermohaline staircase can the average eddy viscosity be estimated? A simple model for momentum transport in such a system shows that the average dissipation and viscosity are controlled by the regions of high dissipation and small eddy viscosity, i.e., the interfaces. The model results are combined with a mechanistic argument for momentum transport across the interfaces by convection-driven internal waves. The average eddy viscosity for the staircase is about 40Jb/N2, where Jb is the buoyancy flux, and N is the buoyancy frequency. By definition the eddy diffusivity of the staircase is -Jb/N2, and so the turbulent Prandtl number is constant and equal to -40. The model predictions are consistent with dissipation measurements in the Bahamas by Larson and Gregg (1983) and imply eddy viscosities of about 10-3 m2/s.