Structure I methane hydrates are formed in situ from water-in-mineral oil emulsions in a high pressure rheometer cell. Viscosity is measured as hydrates form, grow, change under flow, and dissociate. Experiments are performed at varying water volume fraction in the original emulsion (0-0.40), temperature (0-6 degrees C), and initial pressure of methane (750-1500 psig). Hydrate slurries exhibit a sharp increase in viscosity upon hydrate formation, followed by complex behavior dictated by factors including continued hydrate formation, shear alignment, methane depletion/dissolution, aggregate formation, and capillary bridging. Hydrate slurries possess a yield stress and are shear-thinning fluids, which are described by the Cross model. Hydrate slurry viscosity and yield stress increased with increasing water volume fraction. As driving force for hydrate formation decreases (increasing temperature, decreasing pressure), hydrate slurry viscosity increases, suggesting that slower hydrate formation leads to larger and more porous aggregates. In total, addition of water to a methane saturated oil can cause more than a fifty-fold increase in viscosity if hydrates form.