Detailed measurements of mean velocity and velocity fluctuation levels (axial, tangential and radial) have been carried out using a laser Doppler anemometer for fully developed pipe flow of an aqueous solution of Laponite, a synthetic clay. The equilibrium rheological structure of this thixotropic liquid is well characterised by the Herschel-Bulkley model. Velocity profiles calculated for a Herschel-Bulkley fluid prove to be a very accurate representation of the measurements for laminar flow at Reynolds numbers below about 1500. The measured profiles develop an unexplained asymmetry for higher Reynolds numbers until the flow undergoes transition to turbulence. The fluid is drag reducing under turbulent flow conditions with relative levels of tangential and radial turbulence intensity suppressed in comparison with water whilst the axial turbulence intensity is little different. Under all flow conditions it is evident that the fluid rheology is far from structural equilibrium, with values for the apparent yield stress and effective viscosity determined from near-wall velocity measurements considerably below those obtained from a rheometer.