In weakly nonlinear dispersive systems, solitons are spatially localized solutions which propagate without changing shape through a delicate balance between dispersion and self-focusing nonlinear effects. These states have been extensively studied in Bose-Einstein condensates, where interatomic interactions give rise to such nonlinearities. Previous experimental work with matter wave solitons has been limited to static intensity profiles. The creation of matter wave breathers--dispersionless soliton-like states with collective oscillation frequencies driven by attractive mean-field interactions--have been of theoretical interest due to the exotic behaviour of interacting matter wave systems. Here, using an attractively interacting Bose-Einstein condensate, we present the first observation of matter wave breathers. A comparison between experimental data and a cubic-quintic Gross-Pitaevskii equation suggests that previously unobserved three-body interactions may play an important role in this system. The observation of long lived stable breathers in an attractively interacting matter wave system indicates that there is a wide range of previously unobserved, but theoretically predicted, effects that are now experimentally accessible.