One of the most peculiar features of imaging systems is the trade-off between resolution and depth of field. Resolution can be improved by increasing the numerical aperture of the imaging system. However, the range of distances that can be put in sharp focus in a single shot decreases with the square of the numerical aperture. Plenoptic imaging (PI) devices are able to retrieve both spatial and directional information from the scene of interest, usually by placing a microlens array in front of the camera sensor. This feature entails the possibility to refocusing planes of the scene in a much wider range than the natural depth of field of the system, and also to change the point of view on the scene. Though plenoptic imaging is one of the most promising techniques for 3D imaging, its advantages come at the expense of spatial resolution, which can no longer reach the diffraction limit. We experimentally demonstrate that correlations of chaotic light can be exploited to overcome the inverse proportionality between depth of field and resolution, and perform plenoptic imaging at the diffraction limit. We retrieve images by correlating intensity fluctuations at different points of two parts of a sensor, which register spatial and angular information, respectively. Hence, our Correlation Plenoptic Imaging (CPI) protocol does not add any limitation to the native resolution of the imaging system. We show the experimental refocusing, through the CPI procedure, of widely out-of-focus parts of a transmissive test target. Moreover, we determine and test the theoretical limits of CPI in terms of resolution and depth of field, quantifying the improvement with respect to standard imaging and classical PI. We finally comment on future perspectives.