X-ray reflectivity is one of the most important methods for atomic scale studies of interface phenomena such as adsorption, growth, segregation and alloying at liquid/liquid interfaces. Such studies at modern sources, such as free electron lasers, are currently impeded by the lack of dedicated liquid surface diffractometers. Here, we demonstrate that this obstacle can be overcome by an alternative experimental approach that uses the natural curvature of a liquid drop for variation of the angle of incidence. This will allow structural studies with the coherent femtosecond X-ray pulses offered by these new sources as well as at high brilliance synchrotron sources. It will allow unprecedented access to atomic structure at liquid interfaces and is therefore of fundamental importance to interface science in general and liquid interfaces in particular, as well as to biological inspired interfaces, electrochemistry and to the study of water and liquid metals.