Dynamic restructuring and ordering are prevalent in driven many-body systems with long-range interactions, such as sedimenting particles 1-3 , dusty plasmas 4 , flocking animals 5-7 and microfluidic droplets 8 . Yet, understanding such collective dynamics from basic principles is challenging because these systems are not governed by global minimization principles, and because every constituent interacts with many others. Here, we report long-range orientational order of droplet velocities in disordered two-dimensional microfluidic droplet ensembles. Droplet velocities exhibit strong long-range correlation as 1/r 2 , with a four-fold angular symmetry. The two-droplet correlation can be explained by representing the entire ensemble as a third droplet. The correlation amplitude is non-monotonous with density owing to excluded-volume effects. Our study puts forth a many-body problem with long-range interactions that is solvable from first principles owing to the reduced dimensionality, and introduces new experimental tools to address open problems in many-body non-equilibrium systems 9,10 .Physical systems with long-range interactions pose a difficult challenge to both theory and experiment and their understanding is considered an open problem, which has attracted much effort in recent years 9 . Long-range hydrodynamic interactions arise in particle-laden fluids, as the motion of particles relative to the surrounding fluid induces a slowly decaying perturbation of the flow field. When the suspension is enclosed in an effective twodimensional (2D) geometry, such as in confined suspensions 11,12 , electrophoresis in capillaries 13 , protein diffusion in membranes 14 , and microfluidic droplets 15,16 , the hydrodynamic perturbations take the form of long-range dipoles. Such dipolar systems, where the exponent of the spatial decay of the interaction equals the dimension, are known to be marginally strong and have therefore attracted special interest 9 . The marginal nature arises from the logarithmic divergence of the interaction with the system size, which leads to intriguing phenomena such as shape dependence, similar to that of dielectrics or magnetic dipoles 17 .Recently, the collective dynamics of microfluidic droplets has generated a growing interest both as a model system for non-equilibrium dynamics and owing to their practical applications 16,[18][19][20][21][22][23][24][25] . Here we generated a highly dynamic and disordered medium with thousands of uniform water-in-oil droplets flowing in a quasi-2D microfluidic channel of width W = 500 µm and height h = 10 µm. The droplets are shaped as discs of uniform radius in the range R = 7-11 µm (Fig. 1a). They are in contact with the horizontal floor and ceiling and deform the laminar streamlines of the carrier oil while being dragged at a mean velocity of u d = 100-200 µm s −1 that is roughly four times slower than the oil velocity (Fig. 1b,c). The system is driven far from equilibrium by the imposed flow and operates at a low Reynolds number of Re ∼ 10 −4 , where vi...