Laser Doppler anemometry is employed to measure the mean velocity and turbulence intensity in the early turbulence regime of the flow of a dilute polymer solution through a small‐diameter tube. (This regime is initiated at an onset Reynolds number in the subcritical range, above which the polymer additive increases drag, and continues through the transitional Reynolds number range, where a continuous transition to turbulent flow with reduced drag is observed.) When the onset flow rate for early tubulence is exceeded, the mean velocity profile becomes progressively flatter with increasing flow rate. That is, a gradual transition from a laminar profile at onset to a more ’’turbulent‐like’’ profile takes place. Turbulence intensities at the tube centerline are about one half those of a fully developed turbulent flow. The inference is drawn from these results that the onset of eary turbulence corresponds to the flow becoming hydrodynamically unstable due to viscoelastic effects introduced by the polymer additive and that the character of the flow is intermediate between laminar and fully developed turbulent flow.