Variations in the width of a quantum well (QW) are known to be a source of broadening of the exciton line. Using low temperature near-field optical microscopy, we have exploited the dependence of exciton energy on well width to show that in GaAs QWs, these seemingly random well-width fluctuations actually exhibit well-defined order-strong long-range correlations appearing laterally, in the plane of the QW, as well as vertically, between QWs grown one on top of the other. We show that these fluctuations are correlated with the commonly found mound structure on the surface. This is an intrinsic property of molecular beam epitaxial growth.