Three-dimensional mean and RMS bubble and liquid velocity measurements have been obtained in a turbulent, recirculating, bubble-driven liquid flow. Measurements have been made using a three-component laser Doppler anemometer. Bubble column turbulent liquid circulation for the present experiments is due to injection of a single vertical jet of air along the column centerline. Measured distributions of mean and RMS bubble and liquid velocities are consistent with the existence of a toroidal recirculating liquid flow, as is observed in flow visualization. Measured mean circumferential (swirl) velocity is essentially zero. RMS velocities in all three directions are of the same order of magnitude as the mean velocity, with radial RMS velocity being slightly larger than the other two components. Relative velocities between the bubbles and liquid are significant only near the air jet and near the free surface.