We report experimental evidence for a full orbital ordering transition in the two-dimensional lanthanum ruthenate La4Ru2O10. The observable consequences of this orbital ordering include the loss of the Ru local moment, a structural distortion which partitions Ru-O bonds into axially oriented short and long sets, a sharp jump in electrical resistivity, and the opening of a spin gap that is visible in neutron scattering experiments. This is a rare example of a discrete orbital ordering transition in a 4d transition metal oxide and demonstrates that orbital effects can have an influence on the properties of layered ruthenates, a family of compounds that notably includes the p-wave superconductor Sr2RuO4 and the field-tuned quantum critical metamagnet Sr3Ru2O7.