Very long baseline interferometry (VLBI) is a technique for imaging celestial radio emissions by simultaneously observing a source from telescopes distributed across Earth. The challenges in reconstructing images from fine angular resolution VLBI data are immense. The data is extremely sparse and noisy, thus requiring statistical image models such as those designed in the computer vision community. In this paper we present a novel Bayesian approach for VLBI image reconstruction. While other methods often require careful tuning and parameter selection for different types of data, our method (CHIRP) produces good results under different settings such as low SNR or extended emission. The success of our method is demonstrated on realistic synthetic experiments as well as publicly available real data. We present this problem in a way that is accessible to members of the community, and provide a dataset website (vlbiimaging.csail.mit.edu) that facilitates controlled comparisons across algorithms.