Double layer two-dimensional electron systems can exhibit a fascinating collective phase, believed to exhibit both quantum ferromagnetism and excitonic superfluidity, when the layers are sufficiently close together. This unusual phase has recently been found to exhibit tunneling phenomena reminiscent of the Josephson effect. A key element of the theoretical understanding of this bizarre quantum fluid is the existence of linearly dispersing Goldstone collective modes. Using the method of magneto-tunneling spectroscopy, we have demonstrated the existence of these modes. We find the measured velocity to be in reasonable agreement with theoretical estimates.