We experimentally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions range from phi = 0.83 - 0.99, such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. There is little or no dependence of the flow behavior on the area fraction of the system.