The extent of droplet clustering in turbulent clouds has remained largely unquantified, and yet is of possible relevance to precipitation formation and radiative transfer. To that end, data gathered by an airborne holographic instrument are used to explore the three-dimensional spatial statistics of cloud droplet positions in homogeneous stratiform boundary-layer clouds. The three-dimensional radial distribution functions g(r) reveal unambiguous evidence of droplet clustering. Three key theoretical predictions are observed: the existence of positive correlations, onset of correlation in the turbulence dissipation range, and monotonic increase of g(r) with decreasing r. This implies that current theory captures the essential processes contributing to clustering, even at large Reynolds numbers typical of the atmosphere.